Methods and apparatus for generating quantum entanglement

Abstract

There is provided methods and systems for attempting generation of quantum entanglement between a first matter qubit at a first node and a second matter qubit at a second node. Time-bin entanglement processes are performed at each node for generating first and second photons having quantum entanglement with the respective first and second matter qubits. The first photon and the second photon are directed to input ports of an optical coupler comprising a plurality of input ports and a plurality of output ports, the first and second photons arriving at input ports of the optical coupler in a superposition of a first time bin and a second time bin. Photons are detected at single photon detectors in the first time bin and in the second time bin. It is determined whether a photon is detected at any of the single photon detectors in the first time bin, and if no photons are detected at any of the single photon detectors in the first time bin, the time-bin entanglement process is restarted at the first node and the second node.

Description

METHODS AND APPARATUS FOR GENERATING QUANTUM ENTANGLEMENTTECHNICAL FIELD

[0001] The present disclosure relates to methods and apparatus related to the generation of quantum entanglement between matter qubits. The methods and apparatus may find particular application in the generation of quantum entanglement between matter qubits disposed at different nodes of a quantum communication system.BACKGROUND

[0002] Quantum computing utilises quantum mechanical effects such as superposition, interference and entanglement to perform computing tasks. In contrast to classical digital computers, which encode data in binary digits (bits), the basic unit of quantum information used in quantum computing is a qubit. A qubit is a unit of quantum information analogous to a bit in classical computing. However, unlike a classical bit, a qubit is subject to quantum mechanical effects and can exist in a coherent superposition of two states simultaneously.

[0003] To implement quantum computing, qubits are realised as physical qubits. A physical qubit is generally realised by maintaining and manipulating a two-state quantum mechanical physical system. For example, atoms, ions, photons, electrons and / or a superconducting electronic circuits in combination with a suitable control device may be used to realise physical qubits. A quantum computer may maintain and manipulate a plurality of physical qubits, and may encode logical qubits onto the physical qubits to execute quantum algorithms.

[0004] One of the limits to present day quantum computing is the number of physical qubits which can be maintained in a single quantum processor, which may be referred to as a core. For example, for at least some forms of physical qubits there may be a limit to the number of physical qubits which can be incorporated into a single quantum processor or core whilst maintaining the required performance and reliability of the quantum processor core.

[0005] The total number of physical qubits which can be used to execute a quantum algorithm may be increased by providing a plurality of quantum processing cores between which quantum communication links may be established. Such an implementation may be referred to as a multi-core quantum computing system.

[0006] Additionally or alternatively, there may be applications of quantum computers in which a network of quantum computers is provided. Quantum communication links may be established between different quantum computers in order to enable communication of quantum states between different quantum computers in a network.

[0007] Quantum communication links may be established between different quantum processing cores and / or different quantum computers by generating quantum entanglementbetween different physical qubits located at different quantum processing cores and / or different quantum computers. Quantum entanglement between remotely situated physical qubits may additionally or alternatively have utility in sensing applications and / or applications in one or more other fields of quantum technology.

[0008] It is in this context that the present disclosure has been devised.SUMMARY

[0009] In an embodiment, there is provided a method of generating a photon having quantum entanglement with a matter qubit, the method comprising: selecting a matter qubit having energy levels such that the probability of emission of a photon from the matter qubit and the matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2); arranging the matter qubit in a resonant optical cavity configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the cavity and in the excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to the third ground state energy level (GS3); initialising the matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2), wherein the first, second and third ground state energy levels (GS1 , GS2, GS3) comprise energy levels which, in the absence of an excitation and / or control field, remain occupied for a period of time as long as a coherence time of the matter qubit and wherein the excited state energy level (e) comprises an energy level from which a further energy level transition may occur on a timescale less than the coherence time of the matter qubit; exposing the matter qubit to a first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subjecting the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and exposing the matter qubit to a second instance of the excitation field.

[0010] In an embodiment, there is provided a method of generating a photon having quantum entanglement with a matter qubit, the method comprising: arranging the matter qubit in a resonant optical cavity configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the cavity and in an excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); initialising the matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); exposing the matter qubit to a first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to theexcited state energy level (e); subjecting the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and exposing the matter qubit to a second instance of the excitation field.

[0011] According to a first aspect of the present invention, there is provided a method of generating a photon having quantum entanglement with a matter qubit, the method comprising: selecting a matter qubit having energy levels such that the probability of emission of a photon from the matter qubit and the matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2); arranging the matter qubit in a resonant optical cavity configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the cavity and in the excited state energy level (e) , emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to the third ground state energy level (GS3); initialising the matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2); exposing the matter qubit to a first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subjecting the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and exposing the matter qubit to a second instance of the excitation field.

[0012] In an embodiment, when the matter qubit is arranged in the optical cavity and in the excited energy level state (e), the probability of stimulated emission of a photon from the matter qubit and the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3) may be greater than the probability of the matter qubit transitioning from the excited state energy level (E) to the second ground state energy level (GS2).

[0013] In an embodiment, the resonant optical cavity is further configured to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0014] In an embodiment, a length of the resonant optical cavity is tuned to be on resonance with an emission wavelength of the photon emitted by the matter qubit to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0015] In an embodiment, a transition between the excited state energy level (e) and the first ground state energy level (GS1 ) may be forbidden by selection rules.

[0016] In an embodiment, the method may comprise, after exposing the matter qubit to the first instance of an excitation field: subjecting the matter qubit to a control field configured to cause an energy level transition from the third ground state energy level (GS3) to another ground state energy level.

[0017] In an embodiment, the another ground state energy level may comprise the first ground state energy level (GS1 ). The matter qubit may be subjected to the control field configured to cause an energy level transition from the third ground state energy level (GS3) to the first ground state energy level (GS1 ), after the matter qubit is subjected to the control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2).

[0018] In an embodiment, the method may comprise, after exposing the matter qubit to the second instance of the excitation field: subjecting the matter qubit to a control field configured to cause an energy level transition from the third ground state energy level (GS3) to the first ground state energy level (GS1 ).

[0019] In an embodiment, exposing the matter qubit to the first instance and / or the second instance of the excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e) may comprise irradiating the matter qubit with radiation emitted from a first laser. In an embodiment, the subjecting the matter qubit to the control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2) may comprise irradiating the matter qubit with radiation emitted from a second laser, different to the first laser.

[0020] In an embodiment, the radiation from the first laser has a wavelength corresponding to the transition from the second ground state energy level (GS2) to the excited state energy level (e).

[0021] In an embodiment, exposing the matter qubit to the first instance and / or the second instance of the excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e) comprises irradiating the matter qubit with radiation emitted from the first laser and a third laser in a two-photon process.

[0022] In an embodiment, the matter qubit has a plurality of energy manifolds each having a plurality of energy levels, and wherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3).

[0023] In an embodiment, the method may comprise subjecting the matter qubit to a static magnetic field to induce the Zeeman effect in the matter qubit. In an embodiment, the matter qubit has a plurality of energy manifolds each having a plurality of energy levels, wherein the Zeeman effect causes energy splitting of the energy levels within each energy manifold toform a plurality of Zeeman states and wherein the first ground state energy level (GS1 ), second ground state energy level (GS2), the third ground state energy level (GS3) and excited state energy level (e) are selected from the available Zeeman states.

[0024] In an embodiment, the optical cavity and the excitation field may be configured such that exposing the matter qubit to the first instance and / or second instance of the excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e), causes the matter qubit to transition from the second ground state energy level (GS2) to the third ground state energy level (GS3) by a Raman process comprising emission of a photon into the optical cavity.

[0025] In an embodiment, the method of any one of the preceding claims, wherein the matter qubit comprises a trapped ion. In an embodiment, the trapped ion comprises a strontium ion of atomic mass 88 (Sr88+).

[0026] In an embodiment, the Sr88+ ion has a plurality of energy manifolds each having a plurality of energy levels, and wherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3). In an embodiment, the excited state energy level (e) is selected from the 5 2P3 / 2 energy level manifold and the third ground state energy level (GS3) selected from the 4 2D5 / 2 energy level manifold

[0027] In an embodiment, the second ground state energy level (GS2) is selected from the 4 2D3 / 2 energy level manifold and / or wherein the first ground state energy level (GS1 ) is selected from the 5 2S1 / 2 energy level manifold. In an embodiment, the Sr88+ ion is trapped with at least one further trapped ion of another ionic species.

[0028] In an embodiment, the matter qubit comprises a neutral atom. In an embodiment, the neutral atom comprises a neutral Barium atom of atomic mass 138 (Ba138).

[0029] In an embodiment, the excited state energy level (e) is selected from the 6s6p1 P1 energy level manifold and the third ground state energy level (GS3) is selected from the 6s5d1 D2 energy level manifold. In an embodiment, the first ground state energy level (GS1 ) and second ground state energy level (GS2) are each selected from the 6s5d3D energy level manifold.

[0030] In an embodiment, the neutral atom comprises a neutral Ytterbium atom of atomic mass 171 (Yb171 ). In an embodiment, the excited state energy level (e) is selected from the 3D1 , mf =+3 / 2 energy level and the third ground state energy level (GS3) is selected from the 3P0 energy level. In an embodiment, the first ground state energy level (GS1 ) is selected from the 1 S0, mf =-1 / 2 energy level and the second ground state energy level (GS2) is selected from the 1 S0, mf =+1 / 2 energy level.

[0031] In an embodiment, there is provided a system for generating a photon having quantum entanglement with a matter qubit, wherein the system comprises: a resonant opticalcavity for receiving a matter qubit, wherein the optical cavity is configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the optical cavity in an excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); and an interaction means configured to: initialise the matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); expose the matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field.

[0032] In an embodiment, there is provided a system for generating a photon having quantum entanglement with a matter qubit, wherein the system comprises: a matter qubit having energy levels selected such that the probability of emission of a photon from the matter qubit and the matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2); a resonant optical cavity for receiving the matter qubit, wherein the optical cavity is configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the optical cavity in the excited state energy level (e) , emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to the third ground state energy level (GS3); and an interaction means configured to: initialise the matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2), wherein the first, second and third ground state energy levels (GS1 , GS2, GS3) comprise energy levels which, in the absence of an excitation and / or control field, remain occupied for a period of time as long as a coherence time of the matter qubit and wherein the excited state energy level (e) comprises an energy level from which a further energy level transition may occur on a timescale less than the coherence time of the matter qubit; expose the matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e) ; subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field. According to a second aspect of the present invention, there is provided a system for generating a photon having quantum entanglement with a matter qubit, wherein the system comprises: a matter qubit having energy levels selected such that the probability of emission of a photon from the matter qubit and the matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the matter qubit transitioningfrom an excited state energy level (E) to a second ground state energy level (GS2); a resonant optical cavity for receiving the matter qubit, wherein the optical cavity is configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the optical cavity in the excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to the third ground state energy level (GS3); and an interaction means configured to: initialise the matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2); expose the matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field.

[0033] In an embodiment, the resonant optical cavity is further configured to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0034] In an embodiment, a length of the resonant optical cavity is tuned to be on resonance with an emission wavelength of the photon emitted by the matter qubit to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0035] In an embodiment, the energy levels of the matter qubit are selected such that a transition between the excited state energy level (e) and the first ground state energy level (GS1 ) is forbidden by selection rules.

[0036] In an embodiment, the interaction means are further configured, after exposing the matter qubit to the first instance of an excitation field, to subject the matter qubit to a control field configured to cause an energy level transition from the third ground state energy level (GS3) to another ground state energy level.

[0037] In an embodiment, the another ground state energy level comprises the first ground state energy level (GS1 ) and wherein the interaction means is configured to subject the matter qubit to the control field configured to cause an energy level transition from the third ground state energy level (GS3) to the first ground state energy level (GS1 ) after the matter qubit is subjected to the control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2).

[0038] In an embodiment, the interaction means are further configured, after exposing the matter qubit to the second instance of the excitation field, to subject the matter qubit to a control field configured to cause an energy level transition from the third ground state energy level (GS3) to the first ground state energy level (GS1 ).

[0039] In an embodiment, the interaction means is configured to expose the matter qubit to the first instance and / or the second instance of the excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e) by irradiating the matter qubit with radiation emitted from a first laser, and wherein the interaction means is configured to subject the matter qubit to the control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2) by irradiating the matter qubit with radiation emitted from a second laser, different from the first laser.

[0040] In an embodiment, the radiation from the first laser has a wavelength corresponding to the transition from the second ground state energy level (GS2) to the excited state energy level (e).

[0041] In an embodiment, the interaction means is configured to expose the matter qubit to the first instance and / or the second instance of the excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e) by irradiating the matter qubit with radiation emitted from the first laser and a third laser in a two-photon process.

[0042] In an embodiment, the matter qubit is selected to have a plurality of energy manifolds each having a plurality of energy levels, and wherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3).

[0043] In an embodiment, the interaction means is further configured to subject the matter qubit to a static magnetic field to induce the Zeeman effect in the matter qubit.

[0044] In an embodiment, the matter qubit is selected to have a plurality of energy manifolds each having a plurality of energy levels, wherein the Zeeman effect causes energy splitting of the energy levels within each energy manifold to form a plurality of Zeeman states and wherein the first ground state energy level (GS1 ), second ground state energy level (GS2), the third ground state energy level (GS3) and excited state energy level (e) are selected from the available Zeeman states.

[0045] In an embodiment, the optical cavity and the excitation field are configured such that exposing the matter qubit to the first instance and / or second instance of the excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e), causes the matter qubit to transition from the second ground state energy level (GS2) to the third ground state energy level (GS3) by a Raman process comprising emission of a photon into the optical cavity.

[0046] In an embodiment, the matter qubit comprises a trapped ion. In an embodiment, the trapped ion comprises a strontium ion of atomic mass 88 (Sr88+). In an embodiment, the Sr88+ ion has a plurality of energy manifolds each having a plurality of energy levels, andwherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3).

[0047] In an embodiment, the excited state energy level (e) is selected from the 5 2P3 / 2 energy level manifold and the third ground state energy level (GS3) selected from the 42D5 / 2 energy level manifold. In an embodiment, the second ground state energy level (GS2) is selected from the 4 2D3 / 2 energy level manifold and / or wherein the first ground state energy level (GS1 ) is selected from the 5 2S1 / 2 energy level manifold. In an embodiment, the Sr88+ ion is trapped with at least one further trapped ion of another ionic species.

[0048] In an embodiment, the matter qubit comprises a neutral atom. In an embodiment, the neutral atom comprises Barium 138 (Ba138). In an embodiment, the excited state energy level (e) is selected from the 6s6p1 P1 energy level manifold and the third ground state energy level (GS3) selected from the 6s5d1 D2 energy level manifold.

[0049] In an embodiment, the first ground state energy level (GS1 ) and second ground state energy level (GS2) are each selected from the 6s5d3D energy level manifold.

[0050] In an embodiment, the neutral atom comprises a neutral Ytterbium atom of atomic mass 171 (Yb171 ). In an embodiment, the excited state energy level (e) is selected from the 3D1 , mf =+3 / 2 energy level and the third ground state energy level (GS3) is selected from the 3P0 energy level. In an embodiment, the first ground state energy level (GS1 ) is selected from the 1 S0, mf =-1 / 2 energy level and the second ground state energy level (GS2) is selected from the 1 S0, mf =+1 / 2 energy level.

[0051] In an embodiment, there is provided a method of generating quantum entanglement between a first matter qubit disposed at a first node of a system and a second matter qubit disposed at a second node of the system. The method comprises: generating, at the first node, a first photon having quantum entanglement with the first matter qubit, wherein the generating comprises: arranging the first matter qubit in a resonant optical cavity at the first node, wherein the optical cavity is configured to stimulate emission of a photon from the first matter qubit when the first matter qubit is arranged in the optical cavity and in an excited state energy level (e), emission of the photon from the first matter qubit causing the first matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); initialising the first matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); exposing the first matter qubit to a first instance of an excitation field configured to excite the first matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subjecting the first matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and exposing the first matter qubit to a second instance of the excitation field, generating at the secondnode a second photon having quantum entanglement with the second matter qubit. The method further comprises directing the first photon and the second photon to different input ports of an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the generating the first photon at the first node and generating the second photon at the second node comprises generating the first and second photons such that they arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; and detecting photons at single photon detectors each arranged to detect photons output from an output port of the plurality of output ports of the optical coupler in the first time bin and in the second time bin.

[0052] According to a third aspect of the present invention, there is provided a method of generating quantum entanglement between a first matter qubit disposed at a first node of a system and a second matter qubit disposed at a second node of the system, wherein the method comprises: generating, at the first node, a first photon having quantum entanglement with the first matter qubit, wherein the generating comprises: selecting the first matter qubit having energy levels such that the probability of emission of a photon from the first matter qubit and the first matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the first matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2); arranging the first matter qubit in a resonant optical cavity at the first node, wherein the optical cavity is configured to stimulate emission of a photon from the first matter qubit when the first matter qubit is arranged in the optical cavity and in the excited state energy level (e), emission of the photon from the first matter qubit causing the first matter qubit to transition from the excited state energy level (e) to the third ground state energy level (GS3); initialising the first matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2);exposing the first matter qubit to a first instance of an excitation field configured to excite the first matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subjecting the first matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and exposing the first matter qubit to a second instance of the excitation field, generating at the second node a second photon having quantum entanglement with the second matter qubit; directing the first photon and the second photon to different input ports of an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the generating the first photon at the first node and generating the second photon at the second node comprises generating the first and second photons such that they arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; and detecting photons at single photon detectors each arranged to detect photons output from an output port of the plurality of output ports of the optical coupler in the first time bin and in the second time bin.

[0053] In an embodiment, the resonant optical cavity at the second node is further configured to increase the probability of the second matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0054] In an embodiment, a length of the resonant optical cavity at the second node is tuned to be on resonance with an emission wavelength of the photon emitted by the second matter qubit to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0055] In an embodiment, in respect of the second matter qubit a transition between the excited state energy level (e) and the first ground state energy level (GS1 ) is forbidden by selection rules.

[0056] In an embodiment, the second matter qubit has a plurality of energy manifolds each having a plurality of energy levels, and wherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3).

[0057] In an embodiment, the first matter qubit and the second matter qubit may be of the same type. For example, the first matter qubit and the second matter qubit may both comprise an atom of the same species, an ion of the same species, a molecule of the same species and / or a quantum dot of the same type. In other examples, the first matter qubit and the second matter qubit may be of a different type. For example, the first matter qubit and the second matter qubit may comprise atoms of different species, ions of different species, molecules of different species and / or quantum dots of different types.

[0058] In an embodiment, the generating the first photon at the first node and the generating the second photon at the second node may comprise addressing substantially the same or corresponding energy levels of the first matter qubit and the second matter qubit.

[0059] In an embodiment, the method may further comprise: projecting measurements made by the single photon detectors onto a Bell state.

[0060] In an embodiment, the generating at the second node a second photon having quantum entanglement with the second matter qubit may comprise: arranging the second matter qubit in a resonant optical cavity at the second node, wherein the optical cavity is configured to stimulate emission of a photon from the second matter qubit when the second matter qubit is arranged in the optical cavity and in an excited state energy level (e) of the second matter qubit, emission of the photon from the second matter qubit causing the second matter qubit to transition from the excited state energy level (e) of the second matter qubit to a third ground state energy level (GS3) of the second matter qubit; initialising the second matter qubit in a superposition of a first ground state energy level (GS1 ) of the second matter qubit and a second ground state energy level (GS2) of the second matter qubit; exposing the second matter qubit to a first instance of an excitation field for the second matter qubit, theexcitation field for the second matter qubit being configured to excite the second matter qubit from the second ground state energy level (GS2) of the second matter qubit to the excited state energy level (e) of the second matter qubit; subjecting the second matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) of the second matter qubit to the second ground state energy level (GS2) of the second matter qubit; and exposing the second matter qubit to a second instance of the excitation field for the second matter qubit.

[0061] In an embodiment, the generating at the second node a second photon having quantum entanglement with the second matter qubit comprises: selecting the second matter qubit having energy levels such that the probability of emission of a photon from the second matter qubit and the second matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the second matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2); arranging the second matter qubit in a resonant optical cavity at the second node, wherein the optical cavity is configured to stimulate emission of a photon from the second matter qubit when the second matter qubit is arranged in the optical cavity and in an the excited state energy level (e) of the second matter qubit, emission of the photon from the second matter qubit causing the second matter qubit to transition from the excited state energy level (e) of the second matter qubit to a the third ground state energy level (GS3) of the second matter qubit; initialising the second matter qubit in a superposition of a first ground state energy level (GS1 ) of the second matter qubit and a the second ground state energy level (GS2) of the second matter qubit; exposing the second matter qubit to a first instance of an excitation field for the second matter qubit, the excitation field for the second matter qubit being configured to excite the second matter qubit from the second ground state energy level (GS2) of the second matter qubit to the excited state energy level (e) of the second matter qubit; subjecting the second matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) of the second matter qubit to the second ground state energy level (GS2) of the second matter qubit; and exposing the second matter qubit to a second instance of the excitation field for the second matter qubit.

[0062] In an embodiment, the resonant optical cavity at the second node is further configured to increase the probability of the second matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0063] In an embodiment, a length of the resonant optical cavity at the second node is tuned to be on resonance with an emission wavelength of the photon emitted by the second matter qubit to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0064] In an embodiment, in respect of the second matter qubit a transition between the excited state energy level (e) and the first ground state energy level (GS1 ) is forbidden by selection rules.

[0065] In an embodiment, the second matter qubit has a plurality of energy manifolds each having a plurality of energy levels, and wherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3).

[0066] In an embodiment, the first matter qubit and the second matter qubit may comprise matter qubits of the same type.

[0067] In an embodiment, the excited state energy level (e) of the first matter qubit may be the same as the excited state energy level (e) of the second matter qubit.

[0068] In an embodiment, the third ground state energy level (GS3) of the first matter qubit may be the same as the third ground state energy level (GS3) of the second matter qubit.

[0069] In an embodiment, the second ground state energy level (GS2) of the first matter qubit may be the same as the second ground state energy level (GS2) of the second matter qubit.

[0070] In an embodiment, generating, at the first node, a first photon having quantum entanglement with the first matter qubit and generating at the second node, a second photon having quantum entanglement with the second matter qubit may comprise: splitting radiation emitted by an excitation laser into a first portion and a second portion; directing the first portion of the radiation emitted by the excitation laser to be incident on the first matter qubit so as to expose the first matter qubit to the excitation field configured to excite the first matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); and directing the second portion of the radiation emitted by the excitation laser to be incident on the second matter qubit so as to expose the second matter qubit to the excitation field configured to excite the second matter qubit from the second ground state energy level (GS2) to the excited state energy level (e).

[0071] According to a fourth aspect of the present invention, there is provided a system for generating quantum entanglement between a first matter qubit and a second matter qubit, wherein the system comprises: a first node for generating a first photon having quantum entanglement with the first matter qubit, the first node comprising: a first matter qubit having energy levels selected such that the probability of emission of a photon from the first matter qubit and the first matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the first matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2); a first resonant optical cavity for receiving the first matter qubit, wherein the first optical cavity is configured to stimulate emission of a photon from the first matter qubit whenthe first matter qubit is arranged in the optical cavity in the excited state energy level (e), emission of the photon from the first matter qubit causing the first matter qubit to transition from the excited state energy level (e) to the third ground state energy level (GS3); an interaction means configured to: initialise the first matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2); expose the first matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field, a second node for generating a photon having quantum entanglement with the second matter qubit; an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the optical coupler is arranged to receive photons emitted from the first node at a first of the plurality of input ports and photons emitted from the second node at a second of the plurality of input ports; and a plurality of single photon detectors each arranged to detect photons output from an output port of the plurality of output ports in a first time bin and in a second time bin, wherein the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of the first time bin and the second time bin.

[0072] In an embodiment, there is provided a system for generating quantum entanglement between a first matter qubit and a second matter qubit, wherein the system comprises: a first node for generating a first photon having quantum entanglement with the first matter qubit the first node comprising: a first resonant optical cavity for receiving a first matter qubit, wherein the first optical cavity is configured to stimulate emission of a photon from the first matter qubit when the first matter qubit is arranged in the optical cavity in an excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); an interaction means configured to: initialise the first matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); expose the first matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field.

[0073] In an embodiment, the system further comprises a second node for generating a photon having quantum entanglement with the second matter qubit; an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the optical coupler is arranged to receive photons emitted from the first node at a first of the plurality of inputports and photons emitted from the second node at a second of the plurality of input ports; and a plurality of single photon detectors each arranged to detect photons output from an output port of the plurality of output ports in a first time bin and in a second time bin. The first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of the first time bin and the second time bin.

[0074] In an embodiment, the resonant optical cavity is further configured to increase the probability of the first matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3). In an embodiment, a length of the resonant optical cavity is tuned to be on resonance with an emission wavelength of the photon emitted by the first matter qubit to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0075] In an embodiment, in respect of the first matter qubit a transition between the excited state energy level (e) and the first ground state energy level (GS1 ) is forbidden by selection rules.

[0076] In an embodiment, the first matter qubit has a plurality of energy manifolds each having a plurality of energy levels, and wherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3).

[0077] In an embodiment, further comprising a controller configured to project measurements made by the single photon detectors onto a Bell state.

[0078] In an embodiment, the second node comprises: a second matter qubit having energy levels selected such that the probability of emission of a photon from the second matter qubit and the second matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the second matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2); a second resonant optical cavity for receiving the second matter qubit, wherein the second optical cavity is configured to stimulate emission of a photon from the second matter qubit when the second matter qubit is arranged in the optical cavity in the excited state energy level (e), emission of the photon from the second matter qubit causing the second matter qubit to transition from the excited state energy level (e) to the third ground state energy level (GS3); an interaction means configured to: initialise the second matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2); expose the second matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subject the matter qubit to a control field configured to cause an energylevel transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field.

[0079] In an embodiment, the second resonant optical cavity at the second node is further configured to increase the probability of the second matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3). In an embodiment, a length of the second resonant optical cavity at the second node is tuned to be on resonance with an emission wavelength of the photon emitted by the second matter qubit to increase the probability of the second matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0080] In an embodiment, in respect of the second matter qubit a transition between the excited state energy level (e) and the first ground state energy level (GS1 ) is forbidden by selection rules.

[0081] In an embodiment, the second matter qubit has a plurality of energy manifolds each having a plurality of energy levels, and wherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3).

[0082] In an embodiment, the first matter qubit and the second matter qubit comprise matter qubits of the same type.

[0083] In an embodiment, there is provided a method of attempting the generation of a photon having quantum entanglement with a matter qubit, wherein the method comprises: arranging the matter qubit in a resonant optical cavity configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the cavity in an excited state energy level (e,) emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); initialising the matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); and exposing the matter qubit to a first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e).

[0084] According to a fifth aspect of the present invention, there is provided a method of attempting the generation of a photon having quantum entanglement with a matter qubit, wherein the method comprises: selecting a matter qubit having energy levels such that the probability of emission of a photon from the matter qubit and the matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2); arranging the matter qubit in a resonant optical cavity configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the cavity in the excited state energy level (e,) emission of the photonfrom the matter qubit causing the matter qubit to transition from the excited state energy level (e) to the third ground state energy level (GS3); initialising the matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2); and exposing the matter qubit to a first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e).

[0085] In an embodiment, the resonant optical cavity is further configured to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0086] In an embodiment, a length of the resonant optical cavity is tuned to be on resonance with an emission wavelength of the photon emitted by the matter qubit to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3). In an embodiment, a transition between the excited state energy level (e) and the first ground state energy level (GS1 ) is forbidden by selection rules.

[0087] In an embodiment, the matter qubit has a plurality of energy manifolds each having a plurality of energy levels, and wherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3).

[0088] In an embodiment, the matter qubit comprises a trapped ion. In an embodiment, the trapped ion comprises a strontium ion of atomic mass 88 (Sr88+).

[0089] In an embodiment, the Sr88+ ion has a plurality of energy manifolds each having a plurality of energy levels, and wherein the first ground state energy level (GS1 ) is selected to be in a different energy level manifold from the second ground state energy level (GS2) and the third ground state energy level (GS3). In an embodiment, the excited state energy level (e) is selected from the 5 2P3 / 2 energy level manifold and the third ground state energy level (GS3) selected from the 4 2D5 / 2 energy level manifold. In an embodiment, the second ground state energy level (GS2) is selected from the 4 2D3 / 2 energy level manifold and / or wherein the first ground state energy level (GS1 ) is selected from the 5 2S1 / 2 energy level manifold. In an embodiment, the Sr88+ ion is trapped with at least one further trapped ion of another ionic species.

[0090] In an embodiment, the matter qubit comprises a neutral atom. In an embodiment, the neutral atom comprises a neutral Barium atom of atomic mass 138 (Ba138). In an embodiment, the excited state energy level (e) is selected from the 6s6p1 P1 energy level manifold and the third ground state energy level (GS3) selected from the 6s5d1 D2 energy level manifold. In an embodiment, the first ground state energy level (GS1 ) and second ground state energy level (GS2) are each selected from the 6s5d3D energy level manifold.

[0091] In an embodiment, the neutral atom comprises a neutral Ytterbium atom of atomic mass 171 (Yb171 ). In an embodiment, the excited state energy level (e) is selected from the 3D1 , mf =+3 / 2 energy level and the third ground state energy level (GS3) is selected from the 3P0 energy level. In an embodiment, the first ground state energy level (GS1 ) is selected from the 1 S0, mf =-1 / 2 energy level and the second ground state energy level (GS2) is selected from the 1 S0, mf =+1 / 2 energy level.

[0092] In an embodiment, the method further comprises: determining after exposing the matter qubit to the first instance of the excitation field, whether to complete the attempting the generation of a photon having quantum entanglement with a matter qubit.

[0093] In an embodiment, the determining whether to complete the attempting the generation of a photon having quantum entanglement with a matter qubit may comprise determining in dependence on whether a control signal is received for completing and / or restarting the attempting the generation of a photon having quantum entanglement with a matter qubit.

[0094] In an embodiment, the control signal may be generated in dependence on measurements made by single photon detectors after exposing the matter qubit to the first instance of an excitation field.

[0095] In an embodiment, the method comprises: if it is determined to complete the attempting the generation of a photon having quantum entanglement with a matter qubit, subjecting the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and exposing the matter qubit to a second instance of the excitation field.

[0096] In an embodiment, the method comprises: if it is not determined to complete the attempting the generation of a photon having quantum entanglement with a matter qubit, reinitialising the matter qubit in the superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); and exposing the matter qubit to the first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e).

[0097] In an embodiment, there is provided a system for attempting generation of a photon having quantum entanglement with a matter qubit, wherein the system comprises: a resonant optical cavity for receiving a matter qubit, wherein the optical cavity is configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the optical cavity in an excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); and an interaction means configured to: initialise the matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); and expose the matter qubit to a first instance of an excitation field for excitingthe matter qubit from the second ground state energy level (GS2) to the excited state energy level (e).

[0098] According to a sixth aspect of the present invention, there is provided a system for attempting generation of a photon having quantum entanglement with a matter qubit, wherein the system comprises: a matter qubit having energy levels such that the probability of emission of a photon from the matter qubit and the matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2); a resonant optical cavity for receiving the matter qubit, wherein the optical cavity is configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the optical cavity in the excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to the third ground state energy level (GS3); and an interaction means configured to: initialise the matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2); and expose the matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e).

[0099] In an embodiment, the resonant optical cavity is further configured to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0100] In an embodiment, a length of the resonant optical cavity is tuned to be on resonance with an emission wavelength of the photon emitted by the matter qubit to increase the probability of the matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3).

[0101] In an embodiment, the system further comprising a controller configured to: determine after exposing the matter qubit to the first instance of the excitation field, whether to complete the attempting the generation of a photon having quantum entanglement with a matter qubit.

[0102] In an embodiment, the controller is further configured to determine whether to complete the attempting the generation of a photon having quantum entanglement with a matter qubit in dependence on whether a control signal is received for completing and / or restarting the attempting the generation of a photon having quantum entanglement with a matter qubit.

[0103] In an embodiment, the controller is configured to generate the control signal in dependence on measurements made by single photon detectors after exposing the matter qubit to the first instance of an excitation field.

[0104] In an embodiment, if it is determined to complete the attempting the generation of a photon having quantum entanglement with a matter qubit, the interaction means is further configured to: subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field.

[0105] In an embodiment, if it is not determined to complete the attempting the generation of a photon having quantum entanglement with a matter qubit, the interaction means is further configured to: re-initialise the matter qubit in the superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); and expose the matter qubit to the first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e).

[0106] According to a seventh aspect of the present invention, there is provided a method for attempting generation of quantum entanglement between a first matter qubit disposed at a first node and a second matter qubit disposed at a second node, wherein the method comprises: performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit; performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit; directing the first photon and the second photon to input ports of an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the time-bin entanglement processes performed at the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; detecting photons at single photon detectors each arranged to detect photons output from an output port of the plurality of output ports of the optical coupler in the first time bin and in the second time bin; determining whether a photon is detected at any of the single photon detectors in the first time bin; and if no photons are detected at any of the single photon detectors in the first time bin, restarting the time-bin entanglement process at the first node and the second node.

[0107] In an embodiment, restarting the time-bin entanglement process at the first node and the second node may comprise transmitting a control signal for restarting the time-bin entanglement process at the first node and the second node.

[0108] In an embodiment, the method may further comprise determining whether a plurality of photons are detected at the single photon detectors in the first time bin; and if a plurality of photons are detected at the single photon detectors in the first time bin, restarting the timebin entanglement process at the first node and the second node.

[0109] According to an eighth aspect of the present invention, there is provided a method for attempting generation of quantum entanglement between a first matter qubit disposed ata first node and a second matter qubit disposed at a second node, wherein the method comprises: performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit; performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit; directing the first photon and the second photon to input ports of an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the time-bin entanglement processes performed at the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; detecting photons at single photon detectors each arranged to detect photons output from an output port of the plurality of output ports of the optical coupler in the first time bin and in the second time bin; determining whether a plurality of photons are detected at the single photon detectors in the first time bin; and if a plurality of photons are detected at the single photon detectors in the first time bin, restarting the time-bin entanglement process at the first node and the second node.

[0110] In an embodiment, the method further comprises determining whether a plurality of photons are detected at the single photon detectors in the first time bin may comprise determining whether a plurality of photons are detected by one of the single photon detectors in the first time bin.

[0111] In an embodiment, determining whether a plurality of photons are detected at the single photon detectors in the first time bin comprises determining whether photons are detected by a plurality of single photon detectors in the first time bin.

[0112] In an embodiment, restarting the time-bin entanglement process at the first node and the second node comprises transmitting a control signal for restarting the time-bin entanglement process at the first node and the second node.

[0113] In an embodiment, the control signal is transmitted from a first controller forming part of a measurement system. In an embodiment, the control signal is transmitted to a second controller configured to control entanglement scheme processes at the first node and / or second node. In an embodiment, the first and / or second controller forms part of an electronic device.

[0114] In an embodiment, the method further comprises displaying information on an electronic display of the electronic device. In an embodiment, the method further comprises displaying information on an electronic display. In an embodiment, the information comprises a detection result and / or a notification relating to the restarting of the time-bin entanglement process. In an embodiment, the information comprises information relating to one or more attempts at generation of quantum entanglement. In an embodiment, the information comprises a percentage or absolute value of the number of successful and / or failed attemptsat generation of quantum entanglement. In an embodiment, the electronic display displays the information as a function of time over a predetermined time period.

[0115] In an embodiment,, further comprising the step of: outputting information relating to one or more attempts at generation of quantum entanglement. In an embodiment, the step of outputting information relating to one or more attempts at generation of quantum entanglement comprises: entering the information into a log file. In an embodiment, the method further comprises: storing the log file.

[0116] In an embodiment, the information comprises a detection result and / or a notification relating to the restarting of the time-bin entanglement process. In an embodiment, the information comprises a percentage or absolute value of the number of successful and / or failed attempts at generation of quantum entanglement.

[0117] In an embodiment, he performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit comprises: exposing the first matter qubit to a first instance of an excitation field for exciting the first matter qubit to an excited state energy level, the first instance of the excitation field being associated with emission of the first photon in the first time bin; and exposing the first matter qubit to a second instance of the excitation field for exciting the first matter qubit to the excited state energy level, the second instance of the excitation field being associated with emission of the first photon in the second time bin. Restarting the time-bin entanglement process at the first node may comprise restarting the time-bin entanglement process before exposing the first matter qubit to the second instance of the excitation field.

[0118] In an embodiment, the performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit comprises: exposing the second matter qubit to a second instance of an excitation field for exciting the second matter qubit to an excited state energy level, the first instance of the excitation field being associated with emission of the second photon in the first time bin; and exposing the second matter qubit to a second instance of the excitation field for exciting the second matter qubit to the excited state energy level, the second instance of the excitation field being associated with emission of the second photon in the second time bin. Restarting the time-bin entanglement process at the second node may comprise restarting the time-bin entanglement process before exposing the second matter qubit to the second instance of the excitation field.

[0119] In an embodiment, one or both of: performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit; and performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit comprises the steps of: arranging the matter qubit in a resonant optical cavity configured tostimulate emission of a photon from the matter qubit when the matter qubit is arranged in the cavity and in an excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); initialising the matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); exposing the matter qubit to a first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subjecting the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and exposing the matter qubit to a second instance of the excitation field.

[0120] In an embodiment, prior to the step of arranging the matter qubit in a resonant optical cavity, the method comprises: selecting a matter qubit having energy levels such that the probability of emission of a photon from the matter qubit and the matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2).

[0121] In an embodiment, restarting the time-bin entanglement process at the first node and / or the second node comprises restarting the time-bin entanglement process before exposing the first and / or second matter qubit to the second instance of the excitation field.

[0122] According to a ninth aspect of the present invention, there is provided a system for generating quantum entanglement between a first matter qubit and a second matter qubit, wherein the system comprises: a first node for generating a first photon having quantum entanglement with the first matter qubit using a time-bin entanglement process; a second node for generating a second photon having quantum entanglement with the second matter qubit using a time-bin entanglement process; an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the optical coupler is arranged to receive photons emitted from the first node at a first of the plurality of input ports and photons emitted from the second node at a second of the plurality of input ports, wherein the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; a plurality of single photon detectors each arranged to detect photons output from an output port of the plurality of output ports in the first time bin and in the second time bin; and a controller configured to: receive data from the single photon detectors indicative of measurements of photons made by the single photon detectors; determine whether a photon is detected at any of the single photon detectors in the first time bin; and if no photons are detected at any of the single photon detectors in the first time bin, to transmit a control signal for restarting the time-bin entanglement process.

[0123] According to a tenth aspect of the present invention, there is provided a system for generating quantum entanglement between a first matter qubit and a second matter qubit, wherein the system comprises: a first node for generating a first photon having quantum entanglement with the first matter qubit using a time-bin entanglement process; a second node for generating a second photon having quantum entanglement with the second matter qubit using a time-bin entanglement process; an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the optical coupler is arranged to receive photons emitted from the first node at a first of the plurality of input ports and photons emitted from the second node at a second of the plurality of input ports, wherein the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; a plurality of single photon detectors each arranged to detect photons output from an output port of the plurality of output ports in the first time bin and in the second time bin; and a controller configured to: receive data from the single photon detectors indicative of measurements of photons made by the single photon detectors; determine whether a plurality of photons are detected at the single photon detectors in the first time bin; and if a plurality of photons are detected at the single photon detectors in the first time bin, to transmit a control signal for restarting the time-bin entanglement process.

[0124] In an embodiment, the controller is further configured to determine whether a plurality of photons are detected at the single photon detectors in the first time bin by determining whether a plurality of photons are detected by one of the single photon detectors in the first time bin.

[0125] In an embodiment, the controller is further configured to determine whether a plurality of photons are detected at the single photon detectors in the first time bin by determining whether photons are detected by a plurality of single photon detectors in the first time bin.

[0126] In an embodiment, further comprising a second controller operable to receive the transmitted control signal, the second controller being configured to control entanglement scheme processes at the first node and / or second node. In an embodiment, further comprising an electronic device and wherein the controller and / or second controller forms part of an electronic device. In an embodiment, the electronic device further comprises an electronic display configured to display information.

[0127] In an embodiment, the electronic device and / or electronic display is configured to display a detection result and / or a notification relating to the restarting of the time-bin entanglement process.

[0128] In an embodiment, the electronic display is configured to display information relating to one or more attempts at generation of quantum entanglement. In an embodiment, theelectronic display is configured to display a percentage or absolute value of the number of successful and / or failed attempts at generation of quantum entanglement. In an embodiment, the electronic display is configured to display the information as a function of time over a predetermined time period.

[0129] In an embodiment, further configured to output information relating to one or more attempts at generation of quantum entanglement. In an embodiment, further configured to enter the information into a log file. In an embodiment, further configured to store the log file.

[0130] In an embodiment, the information comprises a detection result and / or a notification relating to the restarting of the time-bin entanglement process. In an embodiment, the information comprises a percentage or absolute value of the number of successful and / or failed attempts at generation of quantum entanglement.

[0131] In an embodiment, the first node for generating a first photon having quantum entanglement with the first matter qubit comprises: a first resonant optical cavity for receiving a first matter qubit, wherein the first optical cavity is configured to stimulate emission of a photon from the first matter qubit when the first matter qubit is arranged in the optical cavity in an excited state energy level (e), emission of the photon from the first matter qubit causing the first matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); an interaction means configured to: initialise the first matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); expose the first matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field.

[0132] In an embodiment, further comprising: a first matter qubit having energy levels selected such that the probability of emission of a photon from the first matter qubit and the first matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3) is greater than the probability of the first matter qubit transitioning from the excited state energy level (E) to the second ground state energy level (GS2).

[0133] In an embodiment, the second node for generating a second photon having quantum entanglement with the second matter qubit comprises: a second resonant optical cavity for receiving a second matter qubit, wherein the second optical cavity is configured to stimulate emission of a photon from the second matter qubit when the second matter qubit is arranged in the optical cavity in an excited state energy level (e), emission of the photon from the second matter qubit causing the second matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); an interaction means configured to: initialise the second matter qubit in a superposition of a first ground state energy level(GS1 ) and the second ground state energy level (GS2); expose the second matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field,

[0134] In an embodiment, further comprising: a second matter qubit having energy levels selected such that the probability of emission of a photon from the second matter qubit and the second matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3) is greater than the probability of the second matter qubit transitioning from the excited state energy level (E) to the second ground state energy level (GS2).

[0135] According to an eleventh aspect of the present disclosure there is provided a method for monitoring a system for generating quantum entanglement between a first matter qubit disposed at a first node and a second matter qubit disposed at a second node, wherein the method comprises: repeatedly performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit; repeatedly performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit; directing the first photon and the second photon to input ports of an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein each repetition of the time-bin entanglement processes performed at the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; for each repetition of the time-bin entanglement processes performed at the first node and the second node, detecting photons at single photon detectors each arranged to detect photons output from an output port of the plurality of output ports of the optical coupler in the first time bin and in the second time bin; and determining a rate at which photons are detected by different single photon detectors and in the same time bin.

[0136] In an embodiment, the rate is determined over a plurality of repetitions of the timebin entanglement processes performed at the first node and the second node.

[0137] In an embodiment, determining the rate comprises determining a number of detections by different single photon detectors in the same time bin per unit of time or comprises determining a number of detections by different single photon detectors in the same time bin per number of time-bin entanglement processes performed.

[0138] In an embodiment, the method further comprises adjusting one or more parameters of the time-bin entanglement process for generating a first photon having quantumentanglement with the first matter qubit and / or one or more parameters of the time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit in dependence on the determined rate at which photons are detected by different single photon detectors and in the same time bin. In an embodiment, the method further comprises one or both of: repeatedly performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit; and repeatedly performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit, wherein the time-bin entanglement process comprises the steps of: arranging the respective matter qubit in a resonant optical cavity configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the cavity and in an excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); initialising the respective matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2);exposing the respective matter qubit to a first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subjecting the respective matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and exposing the respective matter qubit to a second instance of the excitation field.

[0139] In an embodiment, the method further comprises, prior to the step of arranging the matter qubit in a resonant optical cavity: selecting a matter qubit having energy levels such that the probability of emission of a photon from the matter qubit and the matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2).

[0140] In an embodiment, the method further comprises displaying information on an electronic display. In an embodiment, the information comprises the determined rate. In an embodiment, the determined rate comprises a current rate or an averaged rate. In an embodiment, the method of any one of claims 6 to 8, wherein the electronic display displays the information as a function of time over a predetermined time period.

[0141] In an embodiment, further comprising the step of: outputting information relating to the determined rate. In an embodiment, the step of outputting information relating to the determined rate comprises: entering the information into a log file. In an embodiment, the method further comprises: storing the log file.

[0142] According to a twelfth aspect of the present invention, there is provided a system for generating quantum entanglement between a first matter qubit and a second matter qubit, wherein the system comprises: a first node for repeatedly generating a first photon havingquantum entanglement with the first matter qubit using a time-bin entanglement process; a second node for repeatedly generating a second photon having quantum entanglement with the second matter qubit using a time-bin entanglement process; an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the optical coupler is arranged to receive photons emitted from the first node at a first of the plurality of input ports and photons emitted from the second node at a second of the plurality of input ports, wherein the first node and the second node are configured, for each repetition of generating a first photon and a second photon, to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; a plurality of single photon detectors each arranged to detect photons output from an output port of the plurality of output ports in the first time bin and in the second time bin; and a controller configured to: receive data from the single photon detectors indicative of measurements of photons made by the single photon detectors; and determine a rate at which photons are detected by different single photon detectors and in the same time bin.

[0143] In an embodiment, the controller is further configured to determine the rate over a plurality of repetitions of the time-bin entanglement processes performed at the first node and the second node.

[0144] In an embodiment, the controller is further configured to determine the rate by determining a number of detections by different single photon detectors in the same time bin per unit of time or by determining a number of detections by different single photon detectors in the same time bin per number of time-bin entanglement processes performed.

[0145] In an embodiment, the controller is further configured to adjust one or more parameters of the time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit and / or one or more parameters of the timebin entanglement process for generating a second photon having quantum entanglement with the second matter qubit in dependence on the determined rate at which photons are detected by different single photon detectors and in the same time bin.

[0146] In an embodiment, the system further comprises an electronic display configured to display information. In an embodiment, the information comprises the determined rate. In an embodiment, the determined rate comprises a current rate or an averaged rate.

[0147] According to a thirteenth aspect of the present invention, there is provided a method for monitoring a system for generating quantum entanglement between a first matter qubit disposed at a first node and a second matter qubit disposed at a second node, the first node being operable to repeatedly perform a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit, the second node being operable to repeatedly perform a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit, and the system beingconfigured to direct the first photon and the second photon to input ports of an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein each repetition of the time-bin entanglement processes performed at the first node and the second node is configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin and for each repetition of the time-bin entanglement processes performed at the first node and the second node, and the system is configured to detect photons at single photon detectors each arranged to detect photons output from an output port of the plurality of output ports of the optical coupler in the first time bin and in the second time bin, the method comprising the step of: determining a rate at which photons are detected by different single photon detectors and in the same time bin.

[0148] In an embodiment, the rate is determined over a plurality of repetitions of the timebin entanglement processes performed at the first node and the second node.

[0149] In an embodiment, determining the rate comprises determining a number of detections by different single photon detectors in the same time bin per unit of time or comprises determining a number of detections by different single photon detectors in the same time bin per number of time-bin entanglement processes performed.

[0150] According to a fourteenth aspect of the present invention, there is provided a monitoring system operable to monitor a quantum communication system, the quantum communication system being configured to generate quantum entanglement between a first matter qubit and a second matter qubit and comprising: a first node for repeatedly generating a first photon having quantum entanglement with the first matter qubit using a time-bin entanglement process; a second node for repeatedly generating a second photon having quantum entanglement with the second matter qubit using a time-bin entanglement process; an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the optical coupler is arranged to receive photons emitted from the first node at a first of the plurality of input ports and photons emitted from the second node at a second of the plurality of input ports, wherein the first node and the second node are configured, for each repetition of generating a first photon and a second photon, to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; and a plurality of single photon detectors each arranged to detect photons output from an output port of the plurality of output ports in the first time bin and in the second time bin; wherein the monitoring system comprises a controller configured to: receive data from the single photon detectors indicative of measurements of photons made by the single photon detectors; and determine a rate at which photons are detected by different single photon detectors and in the same time bin.

[0151] In an embodiment, the controller is further configured to determine the rate over a plurality of repetitions of the time-bin entanglement processes performed at the first node and the second node.

[0152] In an embodiment, the controller is further configured to determine the rate by determining a number of detections by different single photon detectors in the same time bin per unit of time or by determining a number of detections by different single photon detectors in the same time bin per number of time-bin entanglement processes performed.

[0153] According to a fifteenth aspect of the present invention, there is provided a system comprising the monitoring system of the fourteenth aspect and a quantum communication system configured to generate quantum entanglement between a first matter qubit and a second matter qubit and comprising: a first node for repeatedly generating a first photon having quantum entanglement with the first matter qubit using a time-bin entanglement process; a second node for repeatedly generating a second photon having quantum entanglement with the second matter qubit using a time-bin entanglement process; an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the optical coupler is arranged to receive photons emitted from the first node at a first of the plurality of input ports and photons emitted from the second node at a second of the plurality of input ports, wherein the first node and the second node are configured, for each repetition of generating a first photon and a second photon, to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; and a plurality of single photon detectors each arranged to detect photons output from an output port of the plurality of output ports in the first time bin and in the second time bin.

[0154] It will be appreciated from the foregoing disclosure and the following detailed description of the examples that certain features and implementations described as being optional in relation to any given aspect of the disclosure set out above should be understood by the reader as being disclosed also in combination with the other aspects of the present disclosure, where applicable. Similarly, it will be appreciated that any attendant advantages described in relation to any given aspect of the disclosure set out above should be understood by the reader as being disclosed as advantages of the other aspects of the present disclosure, where applicable. That is, the description of optional features and advantages in relation to a specific aspect of the disclosure above is not limiting, and it should be understood that the disclosures of these optional features and advantages are intended to relate to all aspects of the disclosure in combination, where such combination is applicable.BRIEF DESCRIPTION OF THE DRAWINGS

[0155] Certain examples of the present disclosure will now be described, with reference to the accompanying drawings, in which:- FIG. 1 is a schematic illustration of a quantum communication system;- FIG. 2 is a schematic illustration of a portion of a node of a quantum communication system;- FIG. 3 is a schematic illustration of an example of energy levels of an example matter qubit;- FIG. 4 is a flowchart of a method of generating a photon having quantum entanglement with a matter qubit;- FIG. 5A is a schematic illustration of an energy level structure of energy levels of an example matter qubit during a stage of a method of generating a photon having quantum entanglement with the matter qubit;- FIG. 5B is a schematic illustration of an energy level structure of energy levels of an example matter qubit during a further stage of a method of generating a photon having quantum entanglement with the matter qubit;- FIG. 5C is a schematic illustration of an energy level structure of energy levels of an example matter qubit during a still further stage of a method of generating a photon having quantum entanglement with the matter qubit;- FIG. 5D is a schematic illustration of an energy level structure of energy levels of an example matter qubit during a still further stage of a method of generating a photon having quantum entanglement with the matter qubit;- FIG. 5E is a schematic illustration of an energy level structure of energy levels of an example matter qubit during a still further stage of a method of generating a photon having quantum entanglement with the matter qubit;- FIG. 5F is a schematic illustration of an energy level structure of energy levels of an example matter qubit during a still further stage of a method of generating a photon having quantum entanglement with the matter qubit;- FIG. 6 is a schematic illustration of energy levels of an example matter qubit;- FIG. 7 is a schematic illustration of energy levels of an example matter qubit;- FIG. 8 is an energy level diagram of selected energy levels of a Sr88+ ion;- FIG. 9 is an energy level diagram of selected energy levels of a Sr88+ ion;- FIG. 9A is an energy level diagram of selected energy levels of a neutral Ba138 atom;- FIG. 9B is an energy level diagram of selected energy levels of a neutral Yb171 atom;- FIG. 10 is a schematic illustration of a quantum communication system;- FIG. 1 1 is a schematic illustration of an example, measurement system, which may be used in a quantum communication system;- FIG. 12 is a chart depicted possible measurement outcomes corresponding to measurements made by a measurement system;- FIG. 13 is a flowchart of a method for attempting generation of quantum entanglement between a matter qubits disposed at different nodes of a quantum communication system;- FIG. 14 is a flowchart of a method which may be performed at a node of a quantum communication system;- FIG. 15 is a flowchart of a method of monitoring a system for generating entanglement between matter qubits disposed at different nodes of a quantum communication system; and- FIG. 16 is a schematic illustration of an example electronic device.DETAILED DESCRIPTION

[0156] Hereinafter, examples of the disclosure are described with reference to the accompanying drawings. However, it should be appreciated that the disclosure is not limited to the described examples, and all changes and / or equivalents or replacements thereto also belong to the scope of the disclosure. The same or similar reference denotations may be used to refer to the same or similar elements throughout the specification and the drawings.

[0157] As used herein, the terms “have,” “may have,” “include,” or “may include” a feature (e.g., a number, function, operation, or a component such as a part) indicate the existence of the feature and do not exclude the existence of other features. Throughout the description and claims of this specification, the words “comprise” and “contain” and variations of them mean “including but not limited to”, and they are not intended to (and do not) exclude other components, integers or steps. Throughout the description and claims of this specification, the singular encompasses the plural unless the context otherwise requires. In particular,where the indefinite article is used, the specification is to be understood as contemplating plurality as well as singularity, unless the context requires otherwise.

[0158] As used herein, the terms “A or B,” “at least one of A and / or B,” or “one or more of A and / or B” may include all possible combinations of A and B. For example, “A or B,” “at least one of A and B,” “at least one of A or B” may indicate all of (1 ) including at least one A, (2) including at least one B, or (3) including at least one A and at least one B.

[0159] As used herein, the terms “first”, “second” and “third” may modify various components and / or features regardless of importance and do not limit the components and / or features. These terms are only used to distinguish one component and / or feature from another. For example, reference to a first component and / or feature and a second component and / or feature may indicate different components and / or features from each other regardless of the order or importance of the components and / or features.

[0160] It will be understood that when an element (e.g., a first element) is referred to as being (physically, operatively or communicatively) “coupled with / to,” or “connected with / to” another element (e.g., a second element), it can be coupled or connected with / to the other element directly or via a third element.

[0161] The terms as used herein are provided merely to describe some embodiments thereof, but not to limit the scope of other embodiments of the disclosure. It is to be understood that the singular forms “a,” “'an,” and “the” include plural references unless the context clearly dictates otherwise. All terms including technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of the disclosure belong. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealised or overly formal sense unless expressly so defined herein.

[0162] FIG. 1 is a schematic illustration of a quantum communication system 102 comprising a first node 104a, a second node 104b and a measurement system 110. The first node 104a and second node 104b may, for example, comprise different quantum computing cores in a multi-core quantum computing system or may comprise different quantum computers in a quantum network. In general, the nodes 104a, 104b may comprise any component, module, location or similar at which at least one physical qubit is situated. In the example shown in FIG. 1 a first matter qubit 106a is situated at the first node 104a and a second matter qubit 106b is situated at the second node 104b. In some examples, a plurality of matter qubits may be situated at one or more nodes of the quantum communication system 102. A matter qubit as referred to herein comprises a physical qubit which comprises physical matter. For example, a matter qubit may comprise an electronic system which is spatially confined in physical matter. The physical matter may comprise a molecule, atom, ion,ensemble of particles and / or bulk physical matter. An electronic system may comprise one or more electrons and / or holes in a semiconductor which can take on different states such as energy levels and / or spin states. Examples of matter qubits may include (but are not limited to) trapped ions, neutral atoms, and isolated molecules. Such example matter qubits comprise physical matter in which electrons are spatially confined in bound states that are quantised to discrete energy levels. Further examples of matter qubits may include quantum dots. Quantum dots may be realised, for example, as solid-state defect type qubits such as a diamond-defect type qubit (such as a nitrogen-vacancy centre in diamond). Quantum dots may be realised, for example, as dopants implanted in semiconductor nanoparticles (e.g., germanium nanoparticles and / or silicon nanoparticles), and / or electrically gated semiconductor heterostructures (e.g., gallium arsenide two-dimensional electron gas with a gate) .

[0163] A matter qubit may be maintained in a bound state at a node of a quantum communication system 102 and one or more physical properties controlled through use of a suitable interaction means. In some examples, a matter qubit (e.g., the first matter qubit 106a and / or the second matter qubit 106b) may comprise a trapped ion (e.g., an ion located in an ion trap) or a neutral atom. One or more physical properties of a trapped ion or atom may be controlled by exposing the ion or atom to controlled electromagnetic fields. For example, one or more lasers may be used to irradiate a trapped ion or atom in such a way as to promote energy level transitions in the ion or atom.

[0164] Quantum communication links may be established between physical qubits 106a, 106b situated at different nodes 104a, 104b of a quantum communication system 102 by establishing quantum entanglement between the qubits 106a, 106b. Quantum entanglement may be established between qubits which at some point have interacted with each other. However, such a process typically requires spatial proximity between the qubits at the time of entanglement generation. Where the qubits are of a type which are not easily physically transported over significant distances (e.g., when the qubits comprise matter qubits), this restricts the type and distance of quantum communication links which can be established through direct interaction between qubits.

[0165] In order to generate quantum entanglement links between remotely situated qubits, photons may be used to transport locally generated quantum entanglement. For example, quantum entanglement may first be generated between a qubit 106a, 106b situated at a node 104a, 104b and a photon. In this context, a qubit 106a, 106b situated at a node 104a, 104b may be referred to as a stationary qubit and a photon having quantum entanglement with a stationary qubit 106a, 106b may be referred to as a flying (or communication) qubit.

[0166] In the depiction shown in FIG. 1 a first photon 108a is generated having quantum entanglement with the first matter qubit 106a and a second photon 108b is generated having quantum entanglement with the second matter qubit 106b. Mechanisms by which a photoncan be generated having quantum entanglement with a matter qubit will be described in further detail below. Mathematically, a matter qubit and a photon (flying qubit) are maximally entangled if their state can be written as expressed in equation (1 ) below (ignoring relative phase factors in the superposition), where |M2>arebasis states for the first and second matter qubits 106a, 106b respectively and|^2>arebasis states for the first and second photons 108a, 108b respectively.

[0167] In order to generate quantum entanglement between the first matter qubit 106a and the second matter qubit 106b, the photons 108a, 108b may be transported to the measurement system 1 10 via photonic links 1 12. The photonic links 112 may, for example, comprise one or more optical components such as one or more optical fibres. In some examples, photon transport over a photonic link 1 12 may comprise transmission through free space.

[0168] The measurement system 110 is configured to perform a Bell state measurement of the photons arriving at the measurement system 110 (e.g., the first photon 108a and the second photon 108b) . A Bell state measurement of two photons (flying qubits) comprises a projection of the quantum states of the two photons onto one of four Bell states, which represent maximally entangled states. The four maximally entangled Bell states of two qubits are given below in equations (2)-(5).

[0169] There are several different ways in which to perform a Bell state measurement of two photons, which at least partially depend on the way in which a quantum state is encoded onto a photon. In general, both photons may be measured (e.g., using single photon detectors) in such a way that it cannot be determined which of the first photon 108a and the second photon 108b is being measured so that the photons are indistinguishable from each other when measured. The photons may therefore be described as being indistinguishable. For example, the photons may each pass through a beam splitter and a property of the photons (e.g., a polarisation and / or timing) output from the beam splitter measured. The beam splitter functions to erase information related to which path the measured photons have taken such that it cannot be distinguished whether a measured photon originated from the first node 104a or the second node 104b.

[0170] If a Bell state measurement of two photons 108a, 108b generated at different nodes 104a, 104b (each photon having quantum entanglement with a qubit 106a, 106b situated at the respective node 104a, 104b) is successful, then a process referred to as entanglement swapping may be achieved. Successful entanglement swapping results in the entanglement between each matter qubit 106a, 106b and their respective photon 108a, 108b being swapped for quantum entanglement with each other such that the first matter qubit 106a becomes entangled with the second matter qubit 106 b. Qubits which are situated at different nodes 104a, 104b and which have quantum entanglement with each other, form a quantum entanglement or communication link between the first node 104a and the second node 104b.

[0171] Qubits which are entangled with each other have quantum states which are dependent on each other. Such entanglement links have a number of different applications. For example, remote entangled photons may be used to perform distributed quantum computing tasks which may significantly scale up a number of physical qubits which are available to perform quantum computation.

[0172] The generation of quantum entanglement between remote qubits 106a, 106b situated at different nodes 104a, 104b may be characterised by at least a rate at which quantum entanglement is generated and a fidelity of the entanglement. Many applications of remote entanglement links may benefit from one or both of a relatively high rate of entanglement generation and a relatively high entanglement fidelity.

[0173] A rate R at which entanglement can be generated (which may for example be expressed as a number of entangled pairs of qubits which can be generated per unit time) between two nodes may be quantified according to equation (6) below, where T is a time period for an entire attempted entanglement generation process between a single pair of qubits and is an end-to-end collection efficiency of collection of a photon from one matter qubit 106a, 106b.2 r '(6)

[0174] The end-to-end collection efficiency represents the efficiency with which a photon is collected from a matter qubit 106a, 106b and transported to and detected by a detector. The end-to-end collection efficiency can be considered to include contributions from a rate *71 of generation of an entangled photon (flying qubit) per entanglement attempt and an efficiency 72 of collection of the entangled photon, transport of the photon to a detector and detection of the photon. The end-to-end collection efficiency may therefore be expressed as = ^1^2. Typically a plurality of attempts at entanglement generation between qubits will be performed before an entanglement link is successfully generated such that the end-to- end collection efficiency is less than one.

[0175] In many applications of remote quantum entanglement links it is desirable to increase the rate R at which entanglement links can be created. For example, in applications in which remote entanglement links are used to perform distributed quantum computing tasks, a plurality of entanglement links between two or more nodes may need to be generated before a distributed computation task can be performed. In such applications there is typically a limited coherence time during which qubits remain in their quantum states and entanglement between qubits persists. An increase in the rate R at which entanglement links can be created may therefore increase the number of entanglement links which can be generated in a useful timeframe and / or may increase a period of time during which entanglement links can be used whilst the qubits remain coherent. To put it another way, the more often an entanglement link can be successfully generated, the more often the entanglement link can be used for its intended purpose (e.g., to perform a distributed quantum operation).

[0176] The fidelity of an entanglement link is a measure of the extent to which the states of the qubits are correlated with each other. In most applications of quantum entanglement links a higher entanglement fidelity is preferred. For example, one of the potential applications of the generation of entanglement between qubits is for use in distributed quantum computing. Distributed quantum computing may include using entangled qubits to perform compute operations such as the execution of a distributed quantum gate. A distributed quantum gate may comprise a two or more qubit gate, where the two or more qubits are distributed over two or more nodes 104a, 104b with an entanglement link between the qubits.

[0177] Quantum computation typically includes some form of quantum error correction. A physical qubit (e.g., matter qubits 106a, 106b) is subject to physical imperfections which act as sources of error. When the physical qubits are used to perform a quantum computation, such errors may propagate through the computational steps. Quantum error correction maybe used to correct for such errors in physical qubits. Quantum error correction may include the use of a plurality of physical qubits (e.g., matter qubits) acting together as though they are a single logical qubit. Quantum operations may then be structured such that errors introduced at physical qubits are suppressed such that quantum computation on logical qubits is robust against errors at physical qubits.

[0178] A plurality of physical qubits may be configured to act as a single logical qubit, at least in part, by generating entanglement between physical qubits. Quantum entanglement links between physical qubits may therefore be utilised to perform quantum error correction. Quantum entanglement links which have a relatively low entanglement fidelity generally require a relatively large number of physical qubits to behave as a single error robust logical qubit. As entanglement fidelity is increased, the number of physical qubits needed to behave as a single error robust logical qubit is reduced. In such applications it is therefore generally desired to generate entanglement links having relatively high fidelity in order to allow for scaling of the number of logical qubits with fewer physical qubits.

[0179] The fidelity of a quantum entanglement link between remote qubits 106a, 106b at different nodes 104a, 104b depends on the fidelity of the entanglement generated between a matter qubit 106a, 106b and a photon 108a, 108b, the distinguishability of a generated pair of photons 108a, 108b, the quality of classical transmission of the photons 108a, 108b from the matter qubits 106a, 106b to the measurement system 1 10 and the spatial and temporal overlap of the photons 108a, 108b at the measurement system 110. In particular, a relatively high fidelity entanglement link may be generated when the fidelity of the entanglement between the matter qubits 106a, 106b and the generated photons 108a, 108b is relatively high, when the generated photons 108a, 108b are indistinguishable from each other at the point of measurement, when the photons 108a, 108b are transmitted from the matter qubits 106a, 106b to the measurement system 110 in a manner which preserves their entanglement fidelity (e.g., coherent transmission of their quantum state) and when the photons 108a, 108b arrive at the measurement system 1 10 with a relatively high degree of spatial and temporal overlap.

[0180] As was explained above, it may generally be desirable to generate quantum entanglement links between qubits 106a, 106b situated at different nodes 104a, 104b at a relatively fast rate R and with a relatively high fidelity. Methods and apparatus are described herein for generating improved remote entanglement links between matter qubits 106a, 106b.

[0181] FIG. 2 is a schematic illustration of at least a portion of a node 204 at which a photon 210 may be generated having quantum entanglement with a matter qubit 206 situated at the node 204. The node 204 may form a node of a quantum communication system. For example, the node 204 may comprise a node of a quantum communication system 102 of the type described above with reference to FIG. 1 . For example, the node 204 may comprise the first node 104a and / or the second node 104b of the quantum communication system 102 shownin FIG. 1 . In general, the node 204 may comprise any node of a multi-node system in which quantum entanglement is to be generated between matter qubits situated at different nodes.

[0182] The node 204 depicted in FIG. 2 comprises an optical cavity 202 and an interaction means 208. The optical cavity 202 is formed by reflectors 214. The reflectors 214 are arranged to confine photons along a closed path in the optical cavity 202. The optical cavity 202 is arranged to have one or more resonant frequencies (and equivalently wavelengths) at which photons are confined in the optical cavity 202. That is, the optical cavity 202 is arranged to only support specific frequencies and wavelengths of photons.

[0183] The resonant frequencies (and, equivalently, wavelengths) of the optical cavity 202 depend at least in part on the length of the optical cavity (e.g., a distance between reflectors 214). The length of the optical cavity 202 may be tuned to a particular resonant frequency (or equivalently wavelength) for an intended application. For example, the length of the optical cavity 202 may be tuned to be on resonance with an emission wavelength (resulting from an energy level transition) of the matter qubit 206. In this way a photon generation efficiency of a matter qubit 206 situated inside the optical cavity 202 may be increased by the Purcell effect. In some examples, an actuator (such as a piezoelectric transducer) may be used to adjust a length of the optical cavity 202 so as to tune the length of the cavity. The length of the optical cavity may, for example, be tuned in response to measurements of a locking laser.

[0184] The interaction means 208 comprises any suitable apparatus for interacting with the matter qubit 206 so as to control a quantum state of the matter qubit 206. The form of the interaction means 208 will depend on the type of matter qubit which is used. In at least some examples, the interaction means 208 may comprise one or more radiation sources for exposing the matter qubit 206 to controlled pulses of electromagnetic radiation. For example, the interaction means 208 may comprise at least one laser arranged to irradiate the matter qubit 206 with pulses of radiation emitted by the laser. The interaction means 208 may be configured to subject the matter qubit 206 to at least one control field for controlling a quantum state of the matter qubit 206 and to at least one excitation field for exciting the matter qubit 206 from a ground state energy level to an excited state energy level. In some examples, the interaction means 208 may be configured to subject the matter qubit 206 to a magnetic field. For example, the interaction means 208 may be configured to subject the matter qubit 206 to a static magnetic field for inducing Zeeman splitting in energy levels of the matter qubit 206.

[0185] In the depiction shown in FIG. 2, the optical cavity 202 is coupled to a photonic link 1 12. As was described above, with reference to FIG. 1 a photonic link 1 12 may comprise one or more optical components such as one or more optical fibres. In some examples, the photonic link 112 may be configured to facilitate photon transmission through free space. A photon 210 which is emitted from the matter qubit 206 may escape the optical cavity 202 andpass into the photonic link 112 as shown in FIG. 2. For example, at least one of the reflectors 214 may be a partial reflector such that a photon 210 in the optical cavity 202 can be transmitted through the reflector 214 and into the photonic link 112. As was explained above with reference to FIG. 1 , a generated photon 210 may be transported (through the photonic link 1 12) to a measurement system 1 10 at which a Bell state measurement of the photon 210 and a photon generated at another node may be performed.

[0186] In at least some examples described herein, a photon 210 may be emitted from a matter qubit 206 using a so-called A-level structure of energy levels of the matter qubit 206. FIG. 3 is a schematic illustration of an example of a A-level structure of energy levels of the matter qubit 206. The energy level structure includes a second ground state energy level 304 (which is labelled GS2 in FIG. 3), a third ground state energy level 308 (which is labelled GS3 in FIG. 3) and an excited state energy level 306 (which is labelled E in FIG. 3) (the choice of the labels second and third for the ground state energy levels shown in FIG. 3 will become apparent in later described examples which additionally include a first ground state energy level). The second ground state energy level 304 and the third ground state energy level 308 may comprise true energy levels of the matter qubit 206 which may be relatively stable. For example, (in the absence of an excitation and / or control field) the second ground state energy level 304 and the third ground state energy level 308 may be occupied for relatively long periods of time (e.g., as long as the coherence time of the matter qubit 206). As will be described in further detail below, the excited state energy level 306 may be an energy level which is not occupied for long periods of time and from which a further energy level transition may occur on a relatively short timescale (e.g., less than the coherence time of the matter qubit 206).

[0187] Photon emission from the matter qubit 206 may be stimulated by exposing the matter qubit 206 to an excitation field (e.g., by an interaction means 208) which is configured to excite an energy level transition 310 from the second ground state energy level 304 to the excited state energy level 306 of the matter qubit 206. For example, the matter qubit 206 may be irradiated with a pulse of radiation (e.g., emitted from a laser) having a frequency (and equivalently wavelength) configured to stimulate excitation from the second ground state energy level 304 to the excited state energy level 306.

[0188] The matter qubit 206 may be disposed in an optical cavity (e.g., of the form described above with reference to FIG. 2) which is configured to stimulate emission of a photon 210 from the matter qubit 206 so as to cause the matter qubit 206 to undergo a transition 312 from the excited state energy level 306 to the third ground state energy level 308. For example, the optical cavity 202 may be tuned (e.g., its length adjusted) to be on resonance with the wavelength (and equivalently frequency) of a photon 210 emission corresponding tothe transition 312 from the excited state energy level 306 to the third ground state energy level 308.

[0189] The optical cavity 202 may be configured to stimulate emission of a photon 210 from the matter qubit 206 so as to cause the matter qubit 206 to undergo a transition 312 from the excited state energy level 306 to the third ground state energy level 308 before the matter qubit 206 is exposed to the excitation field configured to excite an energy level transition 310 from the second ground state energy level 304 to the excited state energy level 306. In this way the transition from the second ground state energy level 304 to the third ground state energy level 308 (via the excited state energy level 306) may proceed coherently and with substantially no population in the excited state energy level 306. Emission of the photon 210 may comprise emission by a Raman process. An energy level transition of the type shown in FIG. 3 in order to emit a photon 210 from a matter qubit 206 may be performed using vacuum STImulated emission via Raman Adiabatic Passage (v-STIRAP). v-STIRAP processes have been shown to be highly efficient at generating photons in the manner described above.

[0190] As was explained above, a A-level structure of energy levels of a matter qubit 206 may be used to stimulate emission of a photon 210 from the matter qubit 206, where the A- level structure of energy levels includes an excited state energy level 306. Since, the transitions 310, 312 from the second ground state energy level 304 to the excited state energy level 306 proceed coherently with substantially no population in the excited state energy level 306 (e.g., by a Raman process), the excited state energy level 306 which is addressed by the transition 310 and the cavity-assisted transition 312 does not necessarily have to precisely correspond with a true energy state of the matter qubit 206. Put another way, the excited state energy level 306 which is used in A-level structure of energy levels may be in resonance with or out of resonance with a true energy level of the matter qubit 206. The excited state energy level 306 which is used depends on the excitation field (e.g., a frequency and wavelength of a laser used to provide the excitation field) which is used to drive the transition 310 to the excited state energy level 306 and a resonant frequency of the optical cavity 202 (which may be tuned) which drives the transition 312 from the excited state energy level 306 to the third ground state energy level 308. If the energy change of the transition 310 from the second ground state energy level 304 (driven by the excitation field) and the energy change of the transition 312 (driven by the optical cavity 202) to the third ground state energy level 308 substantially coincide at a common excited state energy level 306 then the excited state energy level 306 may be out of resonance (different from) a true energy state of the matter qubit 206. In examples, in which the excited state energy level 306 is out of resonance with a true energy state of the matter qubit 206, the excited state energy level 306 may be referred to as a virtual energy level. References herein to an excited stateenergy level should be understood to encompass a virtual energy level, which is not necessarily in resonance with a true energy level of a matter qubit.

[0191] Stimulated emission of a photon 210 from a matter qubit 206 (such as using a v- STIRAP process) may be used to generate emission of a photon having quantum entanglement with the matter qubit 206. In order to do so, a quantum state needs to be encoded into one or more properties of the photon 210 and the quantum state entangled with a quantum state of the matter qubit 206. Entanglement generation schemes have been proposed in which a polarisation of a generated photon is used as a basis for the quantum state of the photon. However, encoding a quantum state into a polarisation of a photon requires the polarisation to be preserved during transport. Polarisation is often relatively sensitive to a number of different processes, such as transmission through an optical fibre which can change the polarisation state of a photon. Several examples are described herein in which a quantum state is encoded into temporal states of a photon, which may be referred to as time-bin encoding. Time-bin encoding is less sensitive (than polarisation encoding) to polarisation rotation, which may for example occur during photon transmission in an optical fibre, and may therefore be more robust to photon transport in optical fibres.

[0192] FIG. 4 is a flowchart of a method 400 of generating a photon having quantum entanglement with a matter qubit according to examples disclosed herein. The method 400 of FIG. 4 will be described with reference to FIG. 5A-FIG. 5F which are each energy level diagrams of the matter qubit at different stages of a method 400 of generating a photon having quantum entanglement with the matter qubit. Such a method 400 may be referred to as a time-bin entanglement scheme or process.

[0193] The matter qubit 206 has a second ground state energy level 304 (labelled GS2), a third ground state energy level 308 (labelled GS3) and an excited state energy level 306 (labelled E) as was described above with reference to FIG. 3. As was also described above, the second ground state energy level 304, the third ground state energy level 308 and the excited state energy level 306 form a A-level structure of energy levels. Any of the features, energy levels and energy level transitions described above with reference to FIG. 3 may also apply to the example described with reference to FIG. 4 and FIG. 5A-FIG. 5F. For example, a transition 310 from the second ground state energy level 304 to the excited state energy level 306 may be driven by an excitation field (e.g., a laser beam). The transition 312 from the excited state energy level 306 to the third ground state energy level 308 may be driven or enhanced by a suitably configured resonant optical cavity 202 in which the matter qubit 206 is disposed. The excited state energy level 306 may be a true energy level of the matter qubit 206 or may be a virtual energy level which is out of resonance with a true energy level of the matter qubit 206.

[0194] In addition to the energy levels described above with reference to FIG. 3, the matter qubit 206 further includes a first ground state energy level 302 (which is labelled GS1 in FIG. 5A - FIG. 5F). Similarly to the second ground state energy level 304 and the third ground state energy level 308, the first ground state energy level 302 may comprise a true energy level of the matter qubit 206 which may be relatively stable. For example, (in the absence of an excitation and / or control field) the first ground state energy level 302 may be occupied for relatively long periods of time (e.g., as long as the coherence time of the matter qubit 206).

[0195] In the examples described herein the first ground state energy level 302 may represent a l0>state of the matter qubit 206 and second ground state energy level 304 may represent a |1> state of the matter qubit 206.

[0196] At step 402 of the method 400 of FIG. 4 the matter qubit 206 is arranged in a resonant optical cavity 202. The resonant optical cavity 202 may have any of the features and / or components of an optical cavity 202 described above with reference to FIG. 2 and / or FIG. 3. For example, the optical cavity 202 is configured to stimulate emission of photon 210 from the matter qubit 206 when the matter qubit 206 is arranged in the optical cavity 202 and in the excited state energy level 306 (where emission of the photon 210 causes the matter qubit 206 to transition from the excited state energy level 306 to the third ground state energy level 308). The matter qubit 206 is placed in an initial state of being in the first ground state energy level 302 which is depicted in FIG. 5A. For example, the matter qubit 206 may be subjected to a suitable control field (which may, for example, be generated by an interaction means 208) so as to place the matter qubit 206 in the first ground state energy level 302 as shown in FIG. 5A. As was explained above, the first ground state energy level 302 may represent a l°> state of the matter qubit 206 such that the matter qubit 206 is initially placed in the |0> state in FIG. 5A.

[0197] At step 404 of the method 400 of FIG. 4 the matter qubit 206 is initialised in a superposition of the first ground state energy level 302 and the second ground state energy level 304. For example, the matter qubit 206 may be subjected to a suitable control field 506 (which may be referred to as a control pulse) which generates the superposition. The application of a control field 506 to place the matter qubit 206 in a superposition of the first ground state energy level 302 and the second ground state energy level 304 is represented in the energy level diagram of FIG. 5B. The control field 506 may be applied by an interaction means 208. The form of the interaction means 208 and the nature of the control field 506 may depend on the form of the matter qubit 206 but in at least some examples may comprise one or more pulses of a laser beam incident on the matter qubit 206. Adopting the Bloch- sphere representation, the control field 506 may be configured to apply a rotation of between 0 and TT radians on the Bloch sphere. For example, the control field 506 may be configured to apply a rotation of TT / 2 to the matter qubit 206, which may be referred to as a TT / 2 pulse. ATT / 2 rotation or pulse may place the matter qubit 206 in a substantially equal superposition of the first ground state energy level 302 and the second ground state energy level 304. Such a superposition state may be written as equation (7) below.

[0198] The superposition of the matter qubit 206 is represented in FIG. 5B by a first wavefunction portion 502 at the first ground state energy level 302 and a second wavefunction portion 504 at the second ground state energy level 304. The first wavefunction portion 502 represents a portion of a probability distribution associated with the energy of the matter qubit 206 being at the first ground state energy level 302. The second wavefunction portion 504 represents a portion of the probability distribution associated with the energy of the matter qubit 206 being at the second ground state energy level 304. The first wavefunction portion 502 and the second wavefunction portion 504 may represent substantially equal portions of the probability distribution.

[0199] At step 406 of the method 400 of FIG. 4 the matter qubit 206 is exposed to a first instance of an excitation field configured to excite the matter qubit 206 from the second ground state energy level 304 to the excited state energy level 306. The exposure to the excitation field according to step 406 is represented in the energy level diagram of FIG. 5C. The excitation field may be generated by and applied by an interaction means 208. In at least some examples exposing the matter qubit 206 to the excitation field may comprise irradiating the matter qubit 206 with at least one pulse of radiation, which may be generated by a laser. The at least one pulse of radiation may have a wavelength (and equivalently frequency) which at least approximately corresponds with the transition 310 from the second ground state energy level 304 to the excited state energy level 306.

[0200] As was described above, the optical cavity 202 is configured to stimulate emission of a photon from the matter qubit 206 when the matter qubit 206 is in the excited state energy level 306 and to drive a transition 312 from the excited state energy level 306 to the third ground state energy level 308. For example, a length of the optical cavity 202 may be tuned to be on resonance with a photon which is emitted during the transition 312 from the excited state energy level 306 to the third ground state energy level 308 so as to promote the transition 312. The excited state energy level 306 may be a virtual energy level.

[0201] The combined effect of the excitation field which is configured to drive the transition 310 from the second ground state energy level 304 to the excited state energy level 306 and the optical cavity 202 which is configured to drive the transition 312 from the excited state energy level 306 to the third ground state energy level 308 is represented in FIG. 5C. Theexcitation field and optical cavity 202 serve to transfer the second wavefunction portion 504 from the second ground state energy level 304 to the third ground state energy level 308 (via the excited state energy level 306, which may be a virtual energy level). The portion of the probability distribution represented by the second wavefunction portion 504 is therefore associated with a probability of emission of a photon 510 in this step, which will be referred to as an early time bin photon 510. The second wavefunction portion 504 thus becomes entangled with a probability distribution of emission of an early time bin photon 510 since the probability of emission of an early time bin photon 510 is dependent on the second wavefunction portion 504. After this step the state of the system may be expressed as equation (8) below, where in each term the leading ket denotes the matter qubit state and the trailing ket indicates a photon occupation state. The strikethough of the term represents that there is no photon associated with the first wavefunction portion502 in the first ground state energy level 302. The subscript E denotes an "early" photon (i.e., a photon emitted in an early time bin).

[0202] At step 408 of the method 400 of FIG. 4 the matter qubit 206 is subjected to a control field configured to cause an energy level transition 514 from the first ground state energy level 302 to the second ground state energy level 304. Unlike the control field applied in step 404 which only served to transfer a portion of the probability distribution from the first ground state energy level 302 to the second ground state energy level 304, the control field applied in step 408 may be configured to substantially fully transfer the probability distribution from the first ground state energy level 302 to the second ground state energy level 304. For example, the control field applied at step 406 may be configured to cause a rotation of approximately TT radians on the Bloch sphere (which may be referred to as a TT pulse) so as to substantially fully transfer the population of the first ground state energy level 302 to the second ground state energy level 304. In contrast the control field applied at step 404 may be configured to apply a rotation of between 0 and TT radians on the Bloch sphere (e.g., a TT / 2 pulse).

[0203] The control field for driving a transition 514 from the first ground state energy level 302 to second ground state energy level 304 is represented in the energy level diagram of FIG. 5D in which the first wavefunction portion 502 is transferred from the first ground state energy level 302 to the second ground state energy level 304.

[0204] In at least some examples, step 408 of the method 400 of FIG. 4 may further comprise subjecting the matter qubit 206 to a control field configured to cause an energylevel transition 508 from the third ground state energy level 308 to the first ground state energy level 302. The control field configured to cause an energy level transition 508 from the third ground state energy level 308 to the first ground state energy level 302 may be configured to substantially fully transfer the probability distribution from the third ground state energy level 308 to the first ground state energy level 302. For example, the control field may comprise a TT pulse.

[0205] The matter qubit 206 may first be exposed to the control field configured to cause an energy level transition 514 from the first ground state energy level 302 to the second ground state energy level 304 and then subsequently may be exposed to the control field configured to cause an energy level transition 508 from the third ground state energy level 308 to the first ground state energy level 302. The result of these control fields is shown in FIG. 5D in which the first wavefunction portion 502 is transferred to the second ground state energy level 304 and the second wavefunction portion 504 is transferred to the first ground state energy level 302. Consequently, the matter qubit 206 remains in a superposition of states where the energy levels in which the first wavefunction portion 502 and the second wavefunction portion 504 reside are swapped relative to the initial superposition shown in FIG. 5B. After this step the state of the system may be expressed as equation (9) below.

[0206] The control field(s) applied in step 408 may comprise any suitable control field and may, for example, be applied by an interaction means 208. For example, the control field(s) may be applied by way of suitably controlled pulses of radiation (e.g., emitted from one or more lasers).

[0207] At step 410 of the method 400 of FIG. 4 the matter qubit 206 is exposed to a second instance of the excitation field configured to excite the matter qubit 206 from the second ground state energy level 304 to the excited state energy level 306. The exposure to the second instance of the excitation field according to step 410 is represented in the energy level diagram of FIG. 5E. The second instance of the excitation field applied at step 410 may be substantially the same as the first instance of the excitation field applied at step 406 but applied at a later time. The second instance of the excitation field may include any of the features of an excitation field described above with reference to step 406. For example, the second instance of the excitation field may be generated by and applied by an interaction means 208 (which may comprise one or more lasers configured to irradiate the matter qubit 206 with suitable pulses of radiation).

[0208] As was described above with reference to step 406, the optical cavity 202 is configured to drive a transition 312 from the excited state energy level 306 to the third ground state energy level 308. The combined effect of the second instance of the excitation field which is configured to drive the transition 310 from the second ground state energy level 304 to the excited state energy level 306 and the optical cavity 202 which is configured to drive the transition 312 from the excited state energy level 306 to the third ground state energy level 308 is represented in FIG. 5E. The excitation field and optical cavity 202 serve to transfer the first wavefunction portion 502 from the second ground state energy level 304 to the third ground state energy level 308 (via the excited state energy level 306, which may be a virtual level). The portion of the probability distribution represented by the first wavefunction portion 502 is therefore associated with a probability of emission of a photon 512 in this step, which will be referred to as a late time bin photon 512. The first wavefunction portion 502 thus becomes entangled with a probability distribution of emission of a late time bin photon 512 since the probability of emission of an early time bin photon 510 is dependent on the first wavefunction portion 502. After this step the state of the system may be expressed as equation (10) below, where the subscript / . denotes a late photon (i.e., a photon emitted in a late time bin).

[0209] Using the energy level transitions depicted in FIG. 5A - FIG. 5E the matter qubit 206 remains in a superposition of states after the second instance of the excitation field. For example, as shown in FIG. 5E the first wavefunction portion 502 is in a different energy level to the second wavefunction portion 504 therefore maintaining a superposition of states. In the depicted energy level transitions this is realised, at least in part, by transferring the second wavefunction portion 504 from the third ground state energy level 308 to the first ground state energy level 302 after application of the first instance of the excitation field in step 406 (as shown in FIG. 5D. As a result, when the first wavefunction portion 502 transfers to the third ground state energy level 308 by application of the second instance of the excitation field at step 410 (and the configuration of the optical cavity 202), the first wavefunction portion 502 and the second wavefunction portion 504 remain in different energy levels and a superposition of states in maintained. However, in other examples, the second wavefunction portion 504 may not be transferred from the third ground state energy level 308 to the first ground state energy level 302 via the transition 508 shown in FIG. 5D. For example, the second wavefunction portion 504 may instead be transferred (e.g., by application of any suitable control field, such as a TT pulse) to another energy level (such as another ground state energy level) other than the first ground state energy level 302. Inprinciple any suitable energy level may be used for the second wavefunction portion 504 in order to maintain a superposition of states (i.e., such that the first wavefunction portion 502 and second wavefunction portion 504 remain in different energy levels).

[0210] Through the method 400 described above with reference to FIG. 4 and FIG. 5A- FIG. 5E the matter qubit 206 emits a photon 510 / 512 which is in a superposition of an early and late state (corresponding to emission of an early time bin photon 510 and a late time bin photon 512 respectively. The superposition of time bin states of the emitted photon 510 / 512 is entangled with a superposition of energy level states of the matter qubit 206. To put it another way, the matter qubit 206 is placed in a superposition of energy level states and then controlled to emit a photon in a superposition of early and late time bin states, where the superposition of the photon states is entangled with the superposition of the matter qubit 206 energy level states. The method 400 therefore serves to generate a photon 510 / 512 having quantum entanglement with the matter qubit 206. A method 400 as described above with reference to FIG. 4 and FIG. 5A- FIG. 5E may be referred to as a time-bin entanglement scheme or process in which a photon is generated having quantum entanglement with a matter qubit 206.

[0211] As a further optional step (not shown in the flowchart of FIG. 4), the matter qubit 206 may be returned to its original superposition of states. For example, the matter qubit 206 may be subjected to a control field configured to cause an energy level transition 514 from the first ground state energy level 302 to the second ground state energy level 304. The control field configured to cause an energy level transition 514 from the first ground state energy level 302 to the second ground state energy level 304 may be configured to substantially fully transfer the probability distribution from the first ground state energy level 302 to the second ground state energy level 304. For example, the control field may comprise a TT pulse.

[0212] The control field to drive a transition from the first ground state energy level 302 to second ground state energy level 304 is represented in the energy level diagram of FIG. 5F in which the second wavefunction portion 504 is transferred from the first ground state energy level 302 to the second ground state energy level 304.

[0213] The matter qubit 206 may further be subjected a control field configured to cause an energy level transition 508 from the third ground state energy level 308 to the first ground state energy level 302. The control field configured to cause an energy level transition 508 from the third ground state energy level 308 to the first ground state energy level 302 may be configured to substantially fully transfer the probability distribution from the third ground state energy level 308 to the first ground state energy level 302. For example, the control field may comprise a TT pulse.

[0214] Similarly to the steps described above with reference to FIG. 5D, the matter qubit 206 may first be exposed to the control field configured to cause an energy level transition514 from the first ground state energy level 302 to the second ground state energy level 304 and then subsequently may be exposed to the control field configured to cause an energy level transition 508 from the third ground state energy level 308 to the first ground state energy level 302. The result of these control fields is shown in FIG. 5F in which the second wavefunction portion 504 is transferred to the second ground state energy level 304 and the first wavefunction portion 502 is transferred to the first ground state energy level 302. Consequently, the matter qubit 206 is returned to its initial superposition of states with emission of a photon in a superposition of temporal states which is entangled with the superposition of states of the matter qubit 206. After this step the state of the system may be expressed as equation (11 ) below.

[0215] The application of one or more further control fields after step 410 of the method 400 of FIG. 4 (e.g., after the second instance of excitation field corresponding to emission of a late time bin photon 512) may be an optional step since in principle after successful generation of an entangled photon, the matter qubit 206 superposition may utilise any suitable energy levels of the matter qubit 206. For example, the matter qubit 206 may be maintained in the superposition of the third ground state energy level 308 and the first ground state energy level 302 as shown in FIG. 5E. Alternatively, one or both of the first wavefunction portion 502 and second wavefunction portion 504 may be transitioned (e.g., by application of a suitable control field) to any suitable energy level(s) of the matter qubit 206.

[0216] As will be described in further detail below, not every attempt at entanglement generation may be successful. In the event that an attempt at generating an entanglement link is not successful then a method 400 corresponding to the method 400 of FIG. 4 may be performed again in order to attempt to generate an entanglement link again. In such situations the control fields described above with reference to FIG. 5F may be applied in order to return the matter qubit 206 to its original state of superposition (e.g., as shown in FIG. 5B) from which a new attempt at entanglement generation can be made.

[0217] The time-bin entanglement scheme which was described above with reference to FIG. 4 and FIG. 5A - FIG. 5F drives a cavity-assisted emission of a photon 510 / 512 when the matter qubit 206 is placed in an excited state energy level 306. Put another way, the scheme utilises an optical cavity 202 which is configured to stimulate photon emission from the matter qubit 206 when the matter qubit 206 is in the excited state energy level 306. The cavity stimulated emission corresponds to an energy level transition 312 of the matter qubit 206 from the excited state energy level 306 to the third ground state energy level 308. However, there may be other energy level transitions which may be possible from the excited stateenergy level 306. It has been realised that such other energy level transitions may affect a rate R at which entanglement generation may be generated and / or a fidelity of a generated entanglement link. Such energy level transitions will be described with reference to FIG. 6 which is a further energy level diagram of a matter qubit 206 as described herein.

[0218] The energy levels of the matter qubit 206 which are shown in FIG. 6 correspond with the energy levels which were described above with reference to FIG. 3 and FIG. 5A - FIG. 5F. In particular, the energy levels of the matter qubit 206 comprise a first ground state energy level 302, a second ground state energy level 304, a third ground state energy level 308, and an excited state energy level 306. Any of the features of these energy levels which were described above with reference to FIG. 3 and / or FIG. 5A - FIG. 5F may also apply to the energy levels shown in FIG. 6 and no further detailed description with reference to FIG. 6 will be provided.

[0219] As was explained above, the matter qubit 206 may be disposed in an optical cavity 202 which is configured to stimulate emission of a photon 210 from the matter qubit 206 when in the excited state energy level 306 and to drive an energy level transition 312 from the excited state energy level 306 to the third ground state energy level 308. A photon 210 emitted via the transition 312 from the excited state energy level 306 to the third ground state energy level 308 may be substantially on resonance with a cavity mode and may be confined and coupled into a photonic link 1 12 for use in a multi-node quantum communication system as described above. The cavity-assisted transition 312 from the excited state energy level 306 to third ground state energy level 308 is thus promoted by suitable configuration of the optical cavity 202. A photon 210 emitted via the cavity-assisted transition 312 from the excited state energy level 306 to the third ground state energy level 308 may be referred to as a cavity-mode photon.

[0220] Whilst the optical cavity 202 is configured to promote the cavity-assisted transition 312 from the excited state energy level 306 to the third ground state energy level 308 (and emission of a cavity-mode photon), other energy level transitions from the excited state energy level 306 may be possible. For example, a matter qubit 206 excited to the excited state energy level 306 may instead undergo a first decay 602 from the excited state energy level 306 to the second ground state energy level 304.

[0221] A first decay 602 may comprise a spontaneous emission event in which a photon is emitted. This photon emitted by spontaneous emission may be lost to the environment. Having returned to the second ground state energy level 304, the matter qubit 206 may once again be excited to the excited state energy level 306 (by the excitation field) from which it may undergo the transition 312 to the third ground state energy level 308 with emission of a cavity mode photon 210 or may once again undergo the first decay 602 to the second ground state energy level 304. In this way, one or more transitions between the second ground state energy level 304 and the excited state energy level 306 may have occurred prior to emissionof a cavity-mode photon 210. For example, in some situations a plurality of first decays 602 from the excited state energy level 306 to the second ground state energy level 304 (and subsequent excitations from the second ground state energy level 304 to the excited state energy level 306) may occur before a cavity-assisted transition 312 to the third ground state energy level 308 occurs with emission of a cavity mode photon 210.

[0222] An example of a plurality of first decays 602 to the second ground state energy level 304 and subsequent transitions 310 (under an excitation field) back to the excited state energy level 306 is shown schematically in the energy level diagram of FIG. 7. In the example depicted in FIG. 7 the matter qubit 206 undergoes two first decays 602 back to the excited state energy level 306 before undergoing the cavity-assisted transition 312 to the third ground state energy level 308 and emission of a cavity-mode photon 210. As a result, the cavity-mode photon 210 is emitted at a later time than if no first decay 602 back to the second ground state energy level 304 were to occur. In other examples, more or fewer first decays 602 may occur prior to emission of a cavity-mode photon 210.

[0223] A matter qubit 206 undergoing one or more first decays 602 may still result in emission of a cavity-mode photon 210. However, a time at which the cavity-mode photon 210 is emitted may depend on a number of times that the first decay 602 from the excited state energy level 306 to the second ground state energy level 304 (and subsequent excitations from the second ground state energy level 304 to the excited state energy level 306) occurs, which may not be precisely controlled.

[0224] One of the factors which can affect a fidelity of an entanglement link generated by performing a Bell state measurement of two photons at a measurement system 110 is one or more first decays 602. It has been realised that a first decay 602 (and potentially repeated first decays 602) prior to emission of a cavity-mode photon 210 may affect the fidelity of the entanglement between the matter qubit 206 and the generated photon 210. This is because the first decay 602 may comprise a spontaneous emission event which may destroy the qubit superposition, resulting in cavity emission without qubit-photon entanglement. Thus it has been realised that instances of a first decay 602 back to the second ground state energy level 304 may adversely degrade a fidelity with which entanglement links can be generated.

[0225] According to at least some examples disclosed herein it is proposed to select energy levels of the matter qubit 206 such that the cavity-assisted transition 312 from the excited state energy level 306 to the third ground state energy level 308 is faster than a first decay 602 from the excited state energy level 306 back to the second ground state energy level 304. To put it another way, the energy levels of the matter qubit may be selected and / or the optical cavity 202 configured such that a probability of the matter qubit 206 (when excited to the excited state energy level 306) undergoing the cavity-assisted transition 312 from the excited state energy level 306 to the third ground state energy level 308 is greater than a probability of the matter qubit 206 (when excited to the excited state energy level 306)undergoing a first decay 602 back to the second ground state energy level 304. That is, a branching ratio associated with the cavity-assisted transition 310 to the third ground state energy level 308 may be greater than a branching ratio associated with the first decay 602 back to the second ground state energy level 304. In at least some examples, the probability of the matter qubit 206 (when excited to the excited state energy level 306) undergoing the transition 312 from the excited state energy level 306 to the third ground state energy level 308 is greater than a probability of the matter qubit 206 (when excited to the excited state energy level 306) undergoing a first decay 602 back to the second ground state energy level 304, even in the absence of an optical cavity 202. That is, a branching ratio associated with the transition 310 to the third ground state energy level 308 may be greater than a branching ratio associated with the first decay 602 back to the second ground state energy level 304 even in the absence on an optical cavity 202. The optical cavity 202 then acts to further enhance the probability / branching ratio of the transition 310 to the third ground state energy level 308. In this way, the first decay 602 may be suppressed in preference to the cavity- assisted transition 310 and instances of the first decay 602 may be reduced. Consequently, the fidelity of entanglement links generated using the above described entanglement scheme may be increased.

[0226] Returning again to FIG. 6, a matter qubit 206 excited into the first excited state energy level 306 may, in some scenarios, undergo a second decay 604 from the excited state energy level 306 to the first ground state energy level 302. In the entanglement scheme described above, when each of the first and second wavefunction portions 502, 504 are in the second ground state energy level 304 and subjected to an instance of the excitation field, the other of the first and second wavefunction portions 502, 504 is in the first ground state energy level 302 (as can be seen, for example, in FIG. 5C for the first instance of the excitation field and in FIG. 5E for the second instance of the excitation field). In such a situation a second decay 604 from the excited state energy level 306 to the first excited state energy level 306 may collapse the superposition of states in the matter qubit 206 since both the first wavefunction portion 502 and the second wavefunction portion 504 will be in the first ground state energy level 302.

[0227] If a second decay 604 to the first ground state energy level 302 occurs during the first instance of the excitation field (e.g., as an alternative to the cavity-assisted transition 312 during the step depicted in FIG. 5C) then the matter qubit 206 may still emit a cavitymode photon in the late time bin. For example, the control field(s) applied in step 408 (as depicted in FIG. 5D) may transition the wavefunction probability distribution to the second ground state energy level 304 and the second instance of the excitation field applied at step 410 (as depicted in FIG. 5E) may drive a cavity-assisted transition 312 resulting in emission of a late time bin photon 512. However, the matter qubit 206 and the late time bin photon 512 will not be in a superposition of states following the collapse of the superposition causedby the second decay 604. The late time bin photon 512 will not therefore be entangled with the matter qubit 206 and thus may not be used to successfully generate an entanglement link with a matter qubit 206 situated at another node.

[0228] If a second decay 604 to the first ground state energy level 302 occurs during the second instance of the excitation field (e.g., as an alternative to the cavity-assisted transition 312 during the step depicted in FIG. 5E) then no late time bin photon 512 can be generated and the superposition of states in the matter qubit 206 will collapse. Even if an early time bin photon 510 is generated during the first instance of the excitation field, neither the matter qubit 206 or the photon will not be in a superposition of states and thus the photon will not have quantum entanglement with the matter qubit 206. Any generated photon will thus not be entangled with the matter qubit 206 and may not be used to successfully generate an entanglement link with a matter qubit 206 situated at another node.

[0229] As was explained above, the second decay 604 may result in a failed attempt to generate entanglement. The second decay 604 may therefore be considered to adversely affect the rate R at which entanglement links can be generated since it may increase a number of attempts at entanglement generation which may need to be made in order to successfully generate an entanglement link.

[0230] According to at least some examples disclosed herein, it is proposed to select energy levels of the matter qubit 206 such that the second decay 604 from the excited state energy level 306 to the first ground state energy level 302 is forbidden by selection rules. Selection (or transition rules) constrain the possible transitions between quantum states which can occur. Transitions which are permitted or forbidden by selection rules will depend on the type of matter qubit 206 and the type of transitions which occur between energy levels. Specific examples of appropriate energy levels will be provided in more detail below. It has been realised that, more generally, selection rules can be used to select energy levels of a matter qubit so as to prevent a second decay 604 from the excited state energy level 306 to a first ground state energy level 302 which is used to generate a superposition of states in the matter qubit 206.

[0231] In the time-bin entanglement scheme described above with reference to FIG. 4 and FIG. 5A - FIG. 5F, a first ground state energy level 302 can be selected which cannot be directly accessed from the excited state energy level 306 (by having a second decay 604 from the excited state energy level which is forbidden by selection rules) since the scheme does not include an excitation from the first ground state energy level 302 to the excited state energy level 306. As was explained above, the time bin entanglement scheme described herein includes a first instance of an excitation field, application of one or more control fields to bring about energy level transitions in the matter qubit 206 and subsequently a second instance of an excitation field. These steps allow part of a superposition of states to be held in a first ground state energy level 302 which is not accessible from an excited state energylevel 306 (i.e. , a second decay 604 from the excited state energy level 306 to the first ground state energy level 302 is forbidden by selection rules) during both the first instance and second instance of the excitation field. Consequently, at least part of the superposition of states can be protected from unwanted decay. The rate R at which entanglement links can be generated may therefore be improved.

[0232] As was explained above, an entanglement generation rate R and an entanglement fidelity may be improved by selection of energy levels such that one or both of first and second condition are satisfied. The first condition may comprise a condition that a first decay 602 from the excited state energy level 306 to the second ground state energy level 304 has a lower branching ratio (probability) than a cavity-assisted transition 312 to the third ground state energy level 308 (which is accompanied by emission of a cavity-mode photon 210). The second condition may comprise a condition that a second decay 604 from the excited state energy level 306 to the first ground state energy level 302 is excluded by selection rules. Selection of energy levels which satisfy one or both of the first condition and second condition is, at least in part, enabled by the use of three different ground state energy levels in the entanglement scheme. In particular, a separate second ground state energy level 304 and third ground state energy level 308 are used, where the second ground state energy level 304 is an energy level from which the matter qubit 206 is excited to an excited state energy level 306 and the third ground state energy level 308 is an energy level which is addressed by a cavity-assisted transition 312 from the excited state energy level 306. The use of separate second 304 and third 308 ground state energies allows a selection of energy levels which results in a higher probability of a cavity-assisted transition 312 to the third ground state energy level 308 than a first decay 602 back to the second ground state energy level 304 (which may degrade entanglement fidelity). Furthermore, a separate first ground state energy level 302 is used to create a superposition of states in the matter qubit 206. The use of a separate first ground state energy level 302 which does not require any direct transitions to or from the excited state energy level 306 allows the first ground state energy level 302 to be selected such that a second decay 604 from the excited state energy level 306 to the first ground state energy level 302 (which may degrade a rate R at which entanglement links can be generated) is forbidden by selection rules.

[0233] The energy levels of a matter qubit 206 which are selected for each of the first ground state energy level 302, second ground state energy level 304, third ground state energy level 308 and excited state energy level 306 will depend on the form of matter qubit 206 which is used and its energy level structure. Merely by way of an illustrative example, an example will be described in which the matter qubit 206 comprises a strontium ion of atomic mass 88 (Sr88+). Sr88+ ions have particular promise for serving as matter qubits 206 in a quantum communication system. For example, Sr88+ ions exhibit at least one energy level transition at wavelengths which are close to telecommunication wavelengths. This mayallow commercially available equipment and optical components to be used in the quantum communication system. Furthermore Sr88+ ions have been shown to be well trapped in an ion trap along with other ionic species such as Ca40+ and Ca43+. Such ionic species may be useful species for forming matter qubits for performing local computation tasks at a node of a quantum communication system. A node of a quantum communication system may therefore comprise at least one trapped Sr88+ ion and at least one trapped ion of another ionic species such as Ca40+ or Ca43+.

[0234] FIG. 8 is an energy level diagram of several selected energy levels of a Sr88+ ion. The energy level diagram of FIG. 8 shows the fine level energy structure of Sr88+ ion. The energy level structure includes a 52P3 / 2 802 energy level, a 52PI / 2 804 energy level, a 52SI / 2 806 energy level, a 42D5 / 2 808 energy level and a 42D3 / 2810 energy level. These energy levels may be referred to as energy level manifolds (in this instance fine-structure manifolds). Each energy level manifold 802, 804, 806, 808 comprises a plurality of energy levels. In absence of an applied magnetic field each energy level within each energy level manifold 802, 804, 806, 808 are at the same energy (i.e. they are degenerate in energy). As will be shown in further detail below, in the presence of a static magnetic field the Zeeman effect causes energy splitting of each of the energy levels within each energy level manifold such that the energy levels are at different energies. These energy levels within an energy level manifold may be referred to as a Zeeman state.

[0235] Also shown in FIG. 8 are a number of transitions 816, 818, 820, 822, 824 and 826 between the energy levels. Properties of these transitions are shown in the table below. The first column of the table below indicates the reference numeral with which the transition is labelled in FIG. 8. The second and third columns of the table below indicate the two energy levels between which the transition takes place. The fourth column of the table below indicates a wavelength (in nanometres (nm)) corresponding to the transition. The wavelength corresponds to the wavelength of a photon which induces or is generated by the transition. The fifth column of the table below indicates a natural linewidth (in mega-Hertz (MHz)) of the transition. The natural linewidths of the transitions correspond to rates at which they occur.

[0236] A selection of energy levels of a Sr88+ ion which can be used as the first ground state energy level 302, second ground state energy level 304, third ground state energy level 308 and excited state energy level 306 according to an entanglement scheme described herein may be made by selecting an energy level manifold for each energy level and a Zeeman state within an energy level manifold for each energy level.

[0237] According to at least some examples disclosed herein the excited state energy level 306 may be selected from the 52P3 / 2 802 energy level manifold and the third ground state energy level 308 may be selected from the 42D5 / 2 808 energy level manifold. This selection may be made such that a cavity-mode photon 210 emitted as part of the entanglement scheme has a wavelength of 1033 nm due to its proximity to telecommunication wavelengths. This may allow commercially available equipment and optical components to be used in the quantum communication system.

[0238] As was described above, it may be desirable that a probability or branching ratio associated with a first decay 602 from the excited state energy level 306 to the second ground state energy level 304 is less than the probability or branching ratio associated with a transition 312 from the excited state energy level 306 to the third ground state energy level 308 (the first condition described above). The probability or branching ratio associated with the transitions corresponds with the natural linewidths shown in the table above. If the excited state energy level 306 is selected from the 52P3 / 2 802 energy level manifold then the second ground state energy level 304 may be selected from the 42D3 / 2810 energy level manifold. This is because the transition 816 from the 52P3 / 2 802 energy level manifold to the 52SI / 2 806 energy level manifold has a relatively high natural linewidth (22.12 MHz), whereas the transition 824 from the 52P3 / 2 802 energy level manifold to the 42D3 / 2810 energy level manifold has lower natural linewidth (0.14 MHz). In particular, the natural linewidth (0.14 MHz) associated with the transition 824 from the 52P3 / 2 802 energy level manifold to the 42D3 / 2 810 energy level manifold is less than the natural linewidth (1.13 MHz) associated with the transition 826 from the 52P3 / 2 802 energy level manifold to the 42D5 / 2 808 energy level manifold. If the excited state energy level 306 is selected from the 52P3 / 2 802 energy level manifold, the third ground state energy level 308 is selected from the 42D5 / 2 808 energy level manifold and the second ground state energy level 304 is selected from the 42D3 / 2810 energy level manifold, then the first condition described above is therefore satisfied. Accordingly, the fidelity of generated entanglement links may be improved.

[0239] The first ground state energy level 302 may be selected from the 52SI / 2 806 energy level manifold. This selection may be made so that the first ground state energy level 302 is in a different energy level manifold to the other ground state energy levels which may reduce chances of the population of the first ground state energy level 302 during application of the excitation field (during the Raman process driven by the excitation field). It may be further preferable that the transition 514 between the first ground state energy level 302 and the second ground state energy level 304 (which may represent the two qubit states) is addressable using a single laser, which is satisfied by selection of the first ground state energy level 302 from the 52SI / 2 806 energy level manifold.

[0240] FIG. 9 is an energy level diagram of several selected energy levels of a Sr88+ ion subjected to a static magnetic field. The static magnetic field is configured to cause Zeeman splitting of energy level manifolds thereby increasing the number of energy levels and transitions which may be used. The static magnetic field may, for example, have a strength of approximately 60 Gauss.

[0241] The energy level diagram of FIG. 9 includes the same 52P3 / 2 802 energy level manifold, 42D5 / 2 808 energy level manifold, 42D3 / 2810 energy level manifold and 52SI / 2 806 energy level manifold as shown in FIG. 8 and described above. Within each energy level manifold a number of Zeeman levels are shown along with their electronic angular momentum quantum number (m). Different energy level manifolds include different numbers of possible numbers of Zeeman states and values of m.

[0242] The first ground state energy level 302, the second ground state energy level 304, the third ground state energy level 308 and the excited state energy level 306 may be selected by selecting Zeeman states from the choice of energy level manifolds which was described above.

[0243] According to at least some examples, for a Sr88+ ion subjected to a static magnetic field, an appropriate choice of energy levels which has been found for each of the first ground state energy level 302, second ground state energy level 304, third ground state energy level 308 and excited state energy level 306 are listed in the table below. These energy levels are also labelled in FIG. 9 with corresponding reference numbers to those used in the earlier figures.

[0244] The selection of Zeeman states corresponding to the excited state energy level 306 and the first ground state energy level 302 may be made such that a second decay 604 from the excited state energy level 306 to the first ground state energy level 302 is forbidden by selection rules. Selection rules may govern a change in m (Am) which is permitted in transitions between S, P and D energy level manifolds. The permitted Am for each type of transition is listed in the table below, where the last column “permitted Am” indicates values of Am which are permitted by selection rules with all other values of Am being forbidden by selection rules.

[0245] As indicated above, the excited state energy level 306 may be selected as 52P3 / 2, m=-3 / 2 and the first ground state energy level 302 may be selected as 52SI / 2, m=+1 / 2. Such a selection means that a second decay 604 from the excited state energy level 306 to the first ground state energy level 302 would correspond to Am=+2, which as can be seen in the first row of the table above is forbidden by selection rules and thus cannot occur. Such a selection therefore satisfies the second condition described above.

[0246] As further indicated above, the third ground state energy level 308 may be selected as 42D5 / 2, m=-3 / 2. Given the above explained selection for the excited state energy level 306, the selection of the third ground state energy level 308 as 42D5 / 2, m=-3 / 2 may be made such that the cavity-assisted transition from the excited state energy level 306 to the third ground state energy level 308 is a transition of Am=0. Other possible transitions from the excited state energy level 306 of 52P3 / 2, m=-3 / 2 to the 42D5 / 2 energy level manifold which are permitted by selection rules correspond to a transition of Am=+1 to the 42D5 / 2, m=-1 / 2 Zeeman state or Am=-1 to the 42Ds / 2, m=-5 / 2. Transitions in which Am=0 correspond to photon emission which is vertically polarised. Transitions in which Am=+1 or Am=-1 correspond to photon emission which is horizontally polarised. Selection of the third ground state energy level 308 as the 42D5 / 2, m=-3 / 2 Zeeman state may therefore allow the desired cavity-assisted transition 312 from the excited state energy level 306 to the third ground state energy level 308 to be polarisation filtered from the possible Am=+1 and Am=-1 transitions, which may be more practical than spectrally filtering the transitions.

[0247] As further indicated above, the second ground state energy level 304 may be selected as 42D3 / 2, m=-1 / 2. The second ground state energy level 304 should be addressable by an excitation field to drive a transition 310 from the second ground state energy level 304 to the excited state energy level 306. Possible choices in the 42D3 / 2energy level manifold which permit this transition 310 (given the choice of 52P3 / 2, m=-3 / 2 for the excited state energy level 306) are the 42D3 / 2, m=-3 / 2 Zeeman state or the 42D3 / 2, m=-1 / 2 Zeeman state. The 42D3 / 2Jm=-1 / 2 Zeeman state may be selected because the transition 310 from 42D3 / 2, m=-1 / 2 to2P3 / 2, m=-3 / 2 may be driven by radiation (e.g., a laser beam) which propagates parallel to the applied magnetic field rather than propagating parallel to an axis of the optical cavity 202. For engineering reasons, it may easier to arrange components such that the excitation field is produced by radiation (e.g., a laser beam) which propagates parallel to the applied magnetic field and thus the 42D3 / 2, m=-1 / 2 Zeeman state may be selected for the second ground state energy level 304.

[0248] The choice of energy levels listed in the table above gives rise to a number of energy level transitions between energy levels which are utilised in a time-bin entanglement scheme as described above with reference to FIG. 4 and FIG. 5A - FIG. 5F. The transitions which are used are listed in the table below and labelled in FIG. 9 with corresponding reference numbers to those used in the earlier figures to label each transition. Also listed in the table below is the purpose of each transition in the entanglement generation scheme, the type of transition and the change in magnetic quantum number (Am) associated with each transition.

[0249] The energy levels of a Sr88+ ion and the transitions between energy levels listed in the tables above may be used to perform an entanglement generation scheme as described above with reference to FIG. 4 and FIG. 5A - FIG. 5F.

[0250] Using the energy levels and transitions of a Sr88+ ion listed in the table above, the transition 310 from the second ground state energy level 304 to the excited state energy level 306 under an excitation field corresponds to a wavelength of approximately 1004 nm. The excitation field may therefore be realised by exposing the matter qubit 206 to a pulse of radiation having a wavelength of about 1004 nm to drive the transition 310 to the excited state energy level 306.

[0251] The transition 312 from the excited state energy level 306 to the third ground state energy level 308 has a wavelength of about 1033 nm and thus a cavity-mode photon 210 which is generated through this transition 312 will have a wavelength of about 1033 nm.

[0252] A transition from the first ground state energy level 302 to the second ground state energy level 304 is used to provide an initial superposition of states in the matter qubit 206 (e.g., as shown with the control field 506 in FIG. 5B) and to swap part of the superposition from the first ground state energy level 302 to the second ground state energy level 304 in between first and second instances of the control field (e.g., as shown with the transition 514 in FIG. 5D). These transitions 506, 514 correspond to a wavelength of about 687 nm. The control field 506 to establish the initial superposition of states may therefore be produced by applying a TT / 2 pulse at 687 nm. The transition 514 to swap part of the superposition from the first ground state energy level 302 to the second ground state energy level 304 in between first and second instances of the control field (e.g., as shown with the transition 514 in FIG. 5D) may be produced by applying a TT pulse at 687 nm.

[0253] A transition 508 from the third ground state energy level 308 to the second ground state energy level 304 is used to swap part of the superposition from the third ground state energy level 308 to the second ground state energy level 304 (e.g., as shown with the transition 508 in FIG. 5D). This transition 514 corresponds to a wavelength of about 674 nm. The transition 508 to swap part of the superposition from the third ground state energy level 308 to the first ground state energy level 302 in between first and second instances of the control field (e.g., as shown with the transition 514 in FIG. 5D) may be produced by applying a TT pulse at 674 nm.

[0254] As was explained above, the selected energy levels of a Sr88+ ion have been shown to satisfy both the first and second condition described above. In particular, it has been found that a branching ratio (probability) of a first decay 602 from the excited state energy level 306 (52PS / 2, m=-3 / 2) to the second ground state energy level 304 (42D3 / 2, m=-1 / 2) is less than the transition 312 from the excited state energy level 306 (52P3 / 2, m=-3 / 2) to the third ground state energy level 308 (42D5 / 2, m=-3 / 2). Accordingly, the cavity-assisted transition tothe second ground state energy level 304 proceeds faster thereby improving the fidelity of a generated entanglement link.

[0255] Furthermore, a second decay 604 from the excited state energy level 306 (52P3 / 2, m=-3 / 2) to the first ground state energy level 302 (52SI / 2, m=+1 / 2) is forbidden by selection rules. The first ground state energy level 302 is therefore protected from an unwanted decay which may collapse the superposition of states of the matter qubit 206.

[0256] Whilst an illustrative example of appropriate energy levels of a Sr88+ ion has been described above, similar principles and energy levels of other forms of matter qubit 206 may be realised according to the methods and apparatus disclosed herein.

[0257] As described above, the energy levels of the matter qubit 206 which are selected for each of the first ground state energy level 302, second ground state energy level 304, third ground state energy level 308 and excited state energy level 306 will depend on the form of matter qubit 206 which is used and its energy level structure. A further example will now be described in which the matter qubit 206 comprises a neutral atom.

[0258] By way of a further illustrative example, an example will be described in which the matter qubit 206 comprises a neutral Barium atom of atomic mass 138 (Ba138 or138Ba). Neutral barium atoms exhibit at least one energy level transition at wavelengths which are close to telecommunication wavelengths. This may allow commercially available equipment and optical components to be used in the quantum communication system. A node of a quantum communication system may therefore comprise at least one trapped neutral Barium atom. Neutral atoms may be trapped by any suitable techniques; for example, using suitable optical tweezers.

[0259] FIG. 9A is an energy level diagram of several selected energy levels of a neutral Ba138 atom. The energy level diagram of FIG. 9A shows the fine level energy structure of the neutral Ba138 atom. A selection of energy levels of a neutral Ba138 atom which can be used as the first ground state energy level 302, second ground state energy level 304, third ground state energy level 308 and excited state energy level 306 according to an entanglement scheme described herein may be made by selecting an energy level manifold for each energy level and a Zeeman state within an energy level manifold for each energy level.

[0260] According to at least some examples disclosed herein the excited state energy level E 306 may be selected from the 6s6p1Pi 902 energy level manifold and the third ground state energy level GS3 308 may be selected from the 6s5d1D2904 energy level manifold. This selection may be made such that a v-STIRAP cavity-mode photon 906 emitted as part of the entanglement scheme has a wavelength of -1500 nm due to its proximity to telecommunication wavelengths. This may allow commercially available equipment and optical components to be used in the quantum communication system.

[0261] As was described above, it may be desirable that a probability or branching ratio associated with a first decay 908 from the excited state energy level 306 to the second ground state energy level 304 is less than the probability or branching ratio associated with a transition 910 from the excited state energy level 306 to the third ground state energy level 308. In this example, this is achieved by selection of the second ground state energy level GS2 304 from the 6s5d3Di 912 level and, as noted above, the third ground state energy level GS3 308 from the 6s5d1D2904 level. Accordingly, the fidelity of generated entanglement links may be improved.

[0262] The first ground state energy level 302 may be selected from the 6s5d3D2914 energy level manifold. In embodiments, the transition 916 between the first ground state energy level 302 and the second ground state energy level 304 (which represents the two qubit states) may be addressable by a two-photon transition utilising two phase-locked lasers. In other words, the transition 916 is addressable by an excitation field generated by two lasers of different wavelengths.

[0263] As noted above, the energy levels of the neutral Ba138 atom are selected such that the first, second and third ground state energy levels (GS1 , GS2, GS3) comprise energy levels which, in the absence of an excitation and / or control field, remain occupied for a period of time as long as a coherence time of the matter qubit and wherein the excited state energy level (e) comprises an energy level from which a further energy level transition may occur on a timescale less than the coherence time of the matter qubit. In this example, the excited state energy level 902, E 306 has a decay lifetime of the order of 0.25s, whereas the selected GS1 , GS2 and GS3 levels 914, 912, 904 comprise metastable states having lifetimes of the order of 60 seconds.

[0264] It is further noted that the preparation of the neutral Ba138 atom in the metastable state is achieved via transition 918. Transition 918 may comprise a two-photon process from the 6s2 1So 92O level to the GS1 302 6s5d3D2914 level. A transition 922 from the second ground state energy level GS2 304 at the 6s5d3Di 912 level of Ba138 to the excited state energy level E 306 at the selected 6s6p1Pi 902 energy level may be effected by means of a v-STIRAP pump having a wavelength of approximately 1 108 nm. Finally, the transition of the population from GS3 308 (i.e. the 6s5d1D2904 level) to GS1 302 (the 6s5d3D2914) may be effected by transition 924.

[0265] The above example shows how the energy level structure of embodiments of the invention may be implemented in a neutral atom such as Ba138. It is to be understood that variations to this scheme are possible within the scope of the present disclosure. For example, the detailed choice of the Zeeman sublevels can be adapted to the needs of specific optical access and B-field orientation constraints. In embodiments, m=-1 may be chosen for the excited state energy level E 306, m=1 for the first ground state energy level GS1 302,m=0 for the second ground state energy level GS2 and m=-1 for the third ground state energy level GS3 308.

[0266] As described above, the energy levels of the matter qubit 206 which are selected for each of the first ground state energy level 302, second ground state energy level 304, third ground state energy level 308 and excited state energy level 306 will depend on the form of matter qubit 206 which is used and its energy level structure. A further example of a matter qubit 206 in the form of a further neutral atom will now be described.

[0267] By way of a further illustrative example, an example will be described in which the matter qubit 206 comprises a neutral Ytterbium atom of atomic mass 171 (Yb171 or171Yb). Neutral Ytterbium atoms exhibit at least one energy level transition at wavelengths which are close to telecommunication wavelengths. This may allow commercially available equipment and optical components to be used in the quantum communication system. A node of a quantum communication system may therefore comprise at least one trapped neutral Ytterbium atom. Neutral atoms may be trapped by any suitable techniques; for example, using suitable optical tweezers.

[0268] FIG. 9B is an energy level diagram of several selected energy levels of a neutral Yb171 atom. The energy level diagram of FIG. 9B shows the fine level energy structure of the neutral Yb171 atom. A selection of energy levels of a neutral Yb171 atom which can be used as the first ground state energy level 302, second ground state energy level 304, third ground state energy level 308 and excited state energy level 306 according to an entanglement scheme described herein may be made by selecting an energy level manifold for each energy level and a Zeeman state within an energy level manifold for each energy level.

[0269] According to at least some examples disclosed herein the excited state energy level E 306 may be selected from the3Di, mt =+3 / 2 952 energy level manifold and the third ground state energy level GS3 308 may be selected from the3Po 954 energy level manifold. This selection may be made such that a photon 956 emitted as part of the entanglement scheme has a wavelength of 1389 nm due to its proximity to telecommunication wavelengths. This may allow commercially available equipment and optical components to be used in the quantum communication system. The emission of the photon 956 at 1389 nm may be enhanced by selection and use of a suitable optical cavity in the manner of optical cavity 202 described above. The photon 956 thus comprises a cavity-mode photon.

[0270] As was described above, it may be desirable that a probability or branching ratio associated with a first decay 958 from the excited state energy level 306 to the second ground state energy level 304 is less than the probability or branching ratio associated with a transition 960 from the excited state energy level 306 to the third ground state energy level 308 resulting in the emission of the photon 956. In this example, this is achieved by selectionof the second ground state energy level GS2 304 from the1So, mf=+1 / 2 962 level and, as noted above, the third ground state energy level GS3 308 from the3Po, mf=+1 / 2 954 level. Accordingly, the fidelity of generated entanglement links may be improved.

[0271] The first ground state energy level 302 may be selected from the1Somf=-1 / 2 964 energy level manifold. In embodiments, the transition 966 between the first ground state energy level 302 and the second ground state energy level 304 (which represents the two qubit states) may be addressable by a radiofrequency (RF) field to create the desired state superposition.

[0272] As noted above, the energy levels of the neutral Yb171 atom are selected such that the first, second and third ground state energy levels (GS1 , GS2, GS3) comprise energy levels which, in the absence of an excitation and / or control field, remain occupied for a period of time as long as a coherence time of the matter qubit and wherein the excited state energy level (E) comprises an energy level from which a further energy level transition may occur on a timescale less than the coherence time of the matter qubit. In this example, the excited state energy level3Di, mf=+3 / 2 952, E 306 has a relatively short decay lifetime, whereas the selected GS1 , GS2 and GS3 levels 964, 962, 954 comprise metastable states having relatively longer lifetimes.

[0273] The transition from the second ground state energy level GS2 304 at the1So, mf=+1 / 2 962 level of Yb171 to the excited state energy level E 306 at the selected3Di, mf=+3 / 2 952 energy level is achieved by an excitation field involving a two-photon process via a virtual state 970 near the3Pi , mf=+3 / 2 manifold. In other words, the excitation field is generated by an interaction means such as an interaction means 208 which, in this embodiment, comprises two lasers having different wavelengths.

[0274] The two-photon process comprises a first transition 968-1 and a second transition 968-2. The first transition 968-1 is from the second ground state energy level GS2 304 at the1So, mf=+1 / 2 962 level to the virtual state 970 near the3Pi , mf=+3 / 2 manifold and is effected by excitation with a 556 nm laser. The second transition 968-2 is from the3Pi, mt=+3 / 2 virtual state to the excited state energy level E 306 at the selected3Di, mf=+3 / 2 952 energy level and is then effected by excitation with a 1539 nm laser.

[0275] Finally, the transition 974 of the population from GS3 308 (i.e. the3Po, mf=+1 / 2 954 level) to GS1 304 (i.e. the1Somf=-1 / 2 964 level) may be effected by excitation with a laser at 578 nm.

[0276] The above example shows how the energy level structure of embodiments of the invention may be implemented in a neutral atom such as Yb171. It is to be understood that variations to this scheme are possible within the scope of the present disclosure. For example, the detailed choice of the Zeeman sublevels can be adapted to the needs of specific optical access and B-field orientation constraints.

[0277] As was described above with reference to FIG. 1 a photon emitted from a matter qubit and having quantum entanglement with the matter qubit may be used as a flying qubit to generate entanglement between remote matter qubits situated at different nodes. An entanglement scheme as described above with reference to FIG. 4, FIG. 5A - FIG. 5F, FIG. 6 and / or FIG. 7 may be performed at one or more nodes to generate at least one flying qubit photon for generating entanglement between remote matter qubits situated at different nodes. In some examples, a corresponding entanglement scheme may be performed at two nodes (e.g., substantially simultaneously) to generate two flying qubit photons which are transported to a measurement system 110 for a Bell state measurement of the two generated photons.

[0278] FIG. 10 is a schematic illustration of a quantum communication system 1002 according to examples contemplated herein. The quantum communication system 1002 of FIG. 10 includes many of the same or corresponding components to those described above with reference to FIG. 1 and FIG. 2. The same reference numerals are used to denote the same or corresponding components in FIG. 1 , FIG. 2 and FIG. 10. Any of the features or components described above with reference to FIG. 1 and FIG. 2 may also apply to the quantum communication system 1002 of FIG. 10. For example, the quantum communication system 1002 comprises a first node 104a and a second node 104b. A first matter qubit 106a is situated at the first node 104a and a second matter qubit 106b is situated at the second node 104b. Both the first node 104a and the second node 104b comprise an optical cavity 202 (e.g., formed by reflectors 214 as shown in FIG. 10) and an interaction means 208.

[0279] The interaction means 208 of each of the first node 104a and the second node 104b are communicatively coupled to a controller 1004. The controller may, for example, comprise any suitable electronic device such as a computing device (e.g., a classical computing device). The controller 1004 may issue one or more control signals which are sent to the interaction means 208 in order to cause the interaction means 208 to perform an entanglement scheme to generate a photon having quantum entanglement with a matter qubit at each node 104a, 104b. For example, the controller 1004 may be configured to coordinate the performance of an entanglement scheme at the first node 104a to generate a first photon 108a having quantum entanglement with the first matter qubit 106a and the performance of an entanglement scheme at the second node 104b to generate a second photon 108b having quantum entanglement with the second matter qubit 106b.

[0280] An entanglement scheme performed at the first node 104a may include substantially the same or corresponding steps to an entanglement scheme performed at the second node 104b. For example, a method 400 as described above with reference to FIG. 4 and FIG. 5A - FIG. 5E may be performed at both the first node 104a and the second node 104b. The first matter qubit 106a may be of the same type as the second matter qubit 106b. For example, the first matter qubit 106a and the second matter qubit 106b may comprise the same speciesof ion and / or neutral atom. Entanglement schemes performed at the first node 104a and the second node 104b may utilise corresponding matter qubit energy levels at each node. For example, corresponding first ground state energy levels 302, second ground state energy levels 304, third ground state energy levels 308 and / or excited state energy levels 306 of the first matter qubit 106a and the second matter qubit 106b may be used in entanglement schemes performed at the first node 104a and the second node 104b.

[0281] In some examples, different entanglement schemes may be performed at the first node 104a and the second node 104b. However, as was explained above, in order to achieve a remote entanglement link between matter qubits with a high entanglement fidelity, the first photon 108a and the second photon 108b should be indistinguishable from each other. Robustness and photon indistinguishability may be improved by performing the same or corresponding entanglement schemes at each of the first node 104a and the second node 104b. In general, an entanglement scheme performed at the first node 104a and the second node 104b will at least be configured to encode a quantum state into the same basis of generated photons. For example, entanglement schemes may be performed at both the first node 104a and the second node 104b which encode a quantum state into temporal states of generated photons (i.e., they are time-bin entanglement schemes). The first photon 108a and the second photon 108b may both be generated in a superposition of an early time bin and a late time bin.

[0282] The controller 1004 may coordinate the timing of an entanglement scheme performed at the first node 104a with the timing of an entanglement scheme performed at the second node 104b. For example, the entanglement schemes at each node may be performed at times such that the first photon 108a and the second photon 108b arrive at the measurement system 110 each in a superposition of the same early time bin and late time bin.

[0283] In some examples, one or more components may be shared by the interaction means 208 of the first node 104a and the interaction means 208 of the second node 104b. For example, one or more radiation sources (e.g., lasers) may be shared by the interaction means 208 of the first node 104a and the second node 104b. In particular, a radiation source configured to provide an excitation field as described above may be shared by the interaction means 208 of the first node 104a and the second node 104b. For example, an excitation radiation source (e.g., laser) may be arranged to emit one or more pulses of radiation configured to excite the first matter qubit 106a and the second matter qubit 106b to an excited state energy level (e.g., the excited state energy level 306 described above). The radiation output from the radiation source may be split (e.g., by a beam splitter), with a first portion directed to be incident on the first matter qubit 106a and a second portion directed to be incident on the second matter qubit 106b. Using a common radiation source to generate an excitation field at both the first node 104a and the second node 104b may result in anexcitation field at both nodes 104a, 104b having substantially the same frequency (and coordinated timing). Consequently, the first photon 108a and the second photon 108b may have improved indistinguishability.

[0284] In some examples one or more other components and / or radiation sources may be shared by the first node 104a and the second node 104b. For example, a radiation source configured to generate one or more control fields may be shared by the first node 104a and the second node 104b. In some examples, the optical cavity 202 at the first node 104a and the optical cavity 202 at the second node 104b may be configured using one or more shared components. For example, a locking laser may be arranged to emit a locking laser beam which may be split (e.g., by a beam splitter) with a first portion being provided to the first node 104a and a second portion being provided to the second node 104b. The first and second portions of the locking laser beam may be used at the first and second nodes 104a, 104b respectively to tune the lengths of the optical cavities 202 at each node to a decided length. By using the same locking laser beam at the first node 104a and the second node 104b the optical cavities 202 may be tuned to substantially the same lengths and / or resonant frequencies.

[0285] The first matter qubit 106a and the second matter qubit 106b are transported via photonic links 1 12 to the measurement system 110 for performance of a Bell state measurement. FIG. 11 is a schematic illustration of an example, measurement system 1 10, which may be used in a quantum communication system 1002 as contemplated herein. The measurement system 110 comprises an optical coupler 1 102, a first detector 1 104, a second detector 1 106 and a controller 1 108.

[0286] The optical coupler 1 102 comprises at least two input ports 1 110 and at least two output ports 1 112. The optical coupler 1 102 comprises a passive optical element configured to distribute light received at each input port 11 10 between the output ports 1 112. The optical coupler 1102 may be arranged to provide an approximately 50:50 distribution between the output ports 1 112. That is, light incident at each input port 11 10 may be approximately equally distributed between the two output ports 1 1 12. The optical coupler 1 102 may be referred to as a beam splitter, where a beam arriving at each of the input ports 1 110 is split between the output ports 1 112. The optical coupler 1 102 may be realised as a reflective beam splitter comprising a partially reflective surface. Photons arriving at each of the input ports 1 1 10 may then either be transmitted through the partially reflective surface to one of the output ports 1 1 12 or reflected by the partially reflective surface to the other of the output ports 1 112. In some examples, the optical coupler 1 102 may comprise a non-reflective coupler such as a fibre coupler. The optical coupler 1 102 may comprise an interference coupler such as a multimode interference (MMI) coupler.

[0287] The optical coupler 1102 is arranged to receive a first photon 108a (e.g., generated at the first node 104a) at one of the input ports 1 110 and a second photon 108b (e.g.,generated at the second node 104b) at the other of the input ports 1 110. As was described above, the first photon 108a and the second photon 108b may be generated such that they are in a state of superposition of an early time bin and a late time bin. In particular, the first photon 108a and the second photon 108b may arrive at different input ports 1 1 10 of the optical coupler 1 102 both in a superposition of substantially the same early time bin and late time bin.

[0288] The optical coupler 1102 is configured to erase information related to which input port 11 10 the photons 108a, 108b arrive at (and from which node 104a, 104b) they originate. Since light arriving at each input port 1 110 is distributed between the output ports 1 112 (e.g., in an approximately 50:50 ratio) a photon 108a, 108b arriving at each input port 1 110 can be output from either output port 11 12. If the photons 108a, 108b arrive at the optical coupler 1 102 both in a superposition of substantially the same early time bin and late time bin (and are otherwise indistinguishable from each other), it cannot therefore be determined if a photon output from an output port 11 12 originated from the first node 104a or the second node 104b.

[0289] Assuming no photon loss, a pair of photons 108a, 108b arriving at different input ports 11 10 of the optical coupler 1102 and both in a superposition of the same early time bin and late time bin will result in two photons being output from the output ports 11 12. The two photons being output from the output ports 11 12 may be output from the same or different output ports 1 112. The two photons being output from the output ports 1 112 may each be output in either an early time bin or a late time bin.

[0290] The first detector 1 104 is arranged to receive and detect photons output from one of the output ports 1 112 and the second detector 1 106 is arranged to receive and detect photons output from the other of the output ports 1 112. The first detector 1104 and the second detector 1106 may each comprise single photon detectors. Any suitable form of single photon detector may be used. For example, a single photon detector may comprise a superconducting detector (such as a superconducting nanowire single-photon detector) or a semiconductor-based single-photon detector. In at least some examples, the first detector 1 104 and the second detector 1 106 may be of a type having a relatively short dead-time after detection of a first photon and before a second subsequent photon can be detected. Using a detector 1104, 1106 with a relatively short dead-time may allow the same detector 1 104, 1 106 to detect and differentiate between photons in multiple time bins (e.g., in both an early and a late time bin).

[0291] The first detector 1 104 and the second detector 1 106 may output data indicative of measurements made by the respective detector. The data output by the first detector 1 104 and the second detector 1106 may be in any suitable form and may, for example, comprise digital data and / or analogue signals. For example, the data may comprise signal pulsesgenerated by a detector 1 104, 1 106 at a time at which the detector 1104, 1106 has detected a photon.

[0292] The controller 1108 is communicatively coupled to the first detector 1104 and the second detector 1106 and is arranged to receive data from the detectors 1104, 1 106 indicative of the measurements made by the detectors 1 104, 1 106. The controller 1 108 may comprise any suitable electronic device such as a computing device (e.g., a classical computing device). Whilst the controller 1108, which forms part of the measurement system 1 10, is described and depicted as being a separate component to the controller 1004 shown in FIG. 10 in some examples, the functionality of both controllers 1004, 1 108 may be performed by a single device. The controller 1004 and the controller 1108 may at least be communicatively coupled to each other.

[0293] The controller 1108 may function as a measurement analyser and may be configured to project measurements made by the first detector 1104 and second detector 1 106 onto a Bell state. Put another way, the controller 1108 may be configured to determine a Bell state of two photons arriving at the measurement system 110 based on the measurements made by the first detector 1 104 and the second detector 1 106. In particular, the controller 1 108 may be configured to determine a Bell state of two photons based on which of the first detector 1104 and second detector 1106 detect the photons (and hence the output ports 1 1 12 from which the photons are output), and the time bins in which the photons are detected. A mapping of measurement outcomes to Bell states may be predetermined such that the controller 1 108 can determine a Bell state for a pair of photons by mapping measurements made by the first detector 1104 and the second detector 1106 onto Bell states according to predetermined relationships.

[0294] FIG. 12 is a chart 1204 depicted possible measurement outcomes for the measurement system 1 10 of FIG. 11 . The chart 1204 of FIG. 12 is split into sections by dotted lines. Each section of the chart 1204 (enclosed by dotted lines) includes four circles and corresponds to a single possible measurement outcome. Each of the four circles in each section represents a measurement for a particular detector and in a particular time bin. For example, as is indicated by row labels 1206, the upper two circles in each section represent measurements made by the first detector 1104 as denoted by a “1 ” in the row labels 1206 of FIG. 12. The lower two circles in each section represent measurements made by the second detector 1 106 as denoted by a “2” in the row labels 1206 of FIG. 12. As is indicated by column labels 1208, the left-most two circles in each section represent measurements made in an early time bin as denoted by an “E” in the column labels 1208 of FIG. 12 . The right-most two circles in each section represent measurements made in a late time bin as denoted by an “L” in the column labels 1208 of FIG. 12. A circle which contains a “1 ” indicates a detector and time-bin in which one photon is detected. A circle which contains a “2” indicates a detectorand time-bin in which two photons are detected. A circle which does not contain a number indicates a detector and time-bin in which zero photons are detected.

[0295] To provide an illustrative example, the section 1218 which is indicated by an arrow numbered 1218 in FIG. 12 represents a measurement outcome in which one photon is detected by the first detector 1 104 in the early time bin and one photon is detected by the second detector 1106 in the late time bin. The section 1220, which is indicated by an arrow numbered 1220 in FIG. 12, represents a measurement outcome in which one photon is detected by the second detector 1106 in the early time bin and one photon is detected by the second detector 1106 in the late time bin. The section 1222, which is indicated by an arrow numbered 1222 in FIG. 12, represents a measurement outcome in which two photon are detected by the first detector 1104 in the early time bin.

[0296] The possible measurement outcomes (corresponding to sections of the chart 1204 of FIG. 12) are grouped into columns corresponding to their mapping onto Bell states or otherwise. A first subset 1210 of measurement outcomes are grouped in a first column of the chart 1204 of FIG. 12 which is titled with an “X”. The measurement outcomes in this column correspond to measurements of two photons in the same time bin but at different detectors. Any measurements in this column do not correspond to a Bell state and thus any measurement of this form will not lead to successfully generating an entanglement link between remote qubits.

[0297] A second subset 1212 of measurement outcomes are grouped in a second column of the chart 1204 of FIG. 12 which is titled with a "^±". The measurement outcomes in this column correspond to measurements of two photons in the same time bin and at the same detector. Measurement outcomes in this column correspond to either theBell state or the Bell state. Whilst these measurements correspond to a Bell state, which Bell state ( Bell state or the <I Bell state) may not be fully determined by the measurement system 1 10 since both the <A+Bell state and the Bell state correspond to the same measurement outcomes.

[0298] A third subset 1214 of measurement outcomes are grouped in a third column of the chart 1204 of FIG. 12 which is titled with a "+". The measurement outcomes in this column correspond to measurements of two photons in different time bins and at the same detector. Measurement outcomes in this column correspond to theBell state and may be mapped to this Bell state by the controller 1 108.

[0299] A fourth subset 1216 of measurement outcomes are grouped in a fourth column of the chart 1204 of FIG. 12 which is titled with a The measurement outcomes in this column correspond to measurements of two photons in different time bins and at different detectors. Measurement outcomes in this column correspond to the Bell state and may be mapped to this Bell state by the controller 1108.

[0300] As explained above, the measurement outcomes shown in the third subset 1214 and fourth subset 1216 in FIG. 12 can be fully mapped onto a Bell state. Such measurement outcomes may represent successful Bell state measurements which may lead to entanglement swapping and a successful entanglement link being generated between remote qubits.

[0301] The measurement outcomes shown in the second subset 1212 in FIG. 12 are not fully determined in that it cannot be determined whether these measurements correspond to the $+Bell state or the ~ Bell state. Furthermore, theBell state and theBell state correspond to a form of entanglement which is often less useful than theBell states. Moreover, the measurement outcomes shown in the second subset 1212 in FIG. 12 correspond to situations in which two photons arrive at the same detector 1104 and in the same time bin. Some single photon detectors may be able to differentiate between detection of a single photon and detection of two photons in the same time bin and can therefore successfully detect the measurements outcomes shown in the second subset 1212. However, some single photon detectors may not be capable of differentiating between detection of a single photon and detection of two photons in the same time bin. Such detectors may not therefore be able to fully determine the measurement outcomes shown in the second subset 1212 in FIG. 12 since a similar detector output may occur in the case of a single photon being detected and the other photon being lost or not successfully generated or detected. For one or more of these reasons, measurement outcomes shown in the second subset 1212 in FIG. 12 may not be considered to correspond to successful generation of an entanglement link between remote qubits and such results may be discarded .

[0302] The measurement outcomes shown in the first subset 1210 in FIG. 12 do not correspond to a Bell state. Furthermore, for indistinguishable photons the measurement outcomes shown in the first subset 1210 in FIG. 12 should not be observed. This is because, if two photons having the same frequency arrive at the optical coupler 1102 at exactly the same time (in the same time bin), as a result of the Hong-Ou-Mandel effect, the two photons should always leave the optical coupler 1102 in the same output port 1 112. The Hong-Ou- Mandel effect therefore means that two indistinguishable photons should not be measured by different detectors and in the same time bin. Measurement outcomes shown in the first subset 1210 in FIG. 12 may not therefore be considered to correspond to successful generation of an entanglement link between remote qubits and such results may be discarded.

[0303] For two indistinguishable photons 108a, 108b arriving at different input ports 11 10 of the optical coupler 1102 and perfect detection efficiency there is an approximately 50% chance that a measurement outcome in the second subset 1212 (corresponding to the <f+Bell state or the $ Bell state) of measurement outcomes will occur. There is an approximately 25% chance that a measurement outcome in the third subset 1214(corresponding to the Bell state) will occur. There is an approximately 25% chance that a measurement outcome in the fourth subset 1216 (corresponding to the 'A Bell state) will occur. As was described above, only measurement outcomes in the third subset 1214 and fourth subset 1216 (corresponding to the <F+Bell state or the IF Bell state) may be considered to correspond to successful entanglement swapping and successful generation of an entanglement link between the first matter qubit 106a and the second matter qubit 106b. For this reason a maximum of 50% of attempts to generate entanglement links will be successful.

[0304] In practice, many more than 50% of attempts to generate entanglement links may fail. For example, the performance of entanglement schemes at the first node 104a and the second node 104b will not always result in successful generation of entangled photons 108a, 108b at both the first node 104a and the second node 104b. Furthermore, generated photons may not always be successfully coupled into a photonic link 112 and / or photon loss may occur before the photons 108a, 108b arrive at the measurement system 1 10. Furthermore, the measurement system 110 itself will not operate with a 100% collection and detection efficiency. For example, photons may be lost in the optical coupler 1102 and / or may not be successfully detected by either the first detector 1104 or second detector 1 106. For these and / or other reasons a relatively high proportion of attempts to generate entanglement links will be unsuccessful and a plurality of attempts may need to be performed in order to successfully generate an entanglement link.

[0305] Each unsuccessful attempt to generate an entanglement link will take some period of time. For example, a full attempt to generate an entanglement link (e.g., performing entanglement schemes at each of a first node 104a and a second node 104b and performing measurements and measurement analysis at the measurement system 110) may take a period of time of the order of thousands of nanoseconds (ns). For example, a full attempt to generate an entanglement link may take between about 2000 and 3000 ns. Each unsuccessful attempt to generate an entanglement link will adversely affect the rate R at which entanglement links can be generated. In particular, the rate R at which entanglement links can be generated will depend both on a number of attempts at entanglement link generation which are needed per successful entanglement link generation and a time taken for each entanglement link generation attempt.

[0306] It has been realised that a time taken to perform an unsuccessful attempt to generate an entanglement link can be reduced by using information obtained during measurements corresponding to the early time bin. FIG. 13 is a flowchart of a method 1300 for attempting generation of quantum entanglement between a first matter qubit 106a disposed at a first node 104a and a second matter qubit 106b disposed at a second node 104b. The method 1300 may be performed in a quantum communication system 1002 as described herein. Forexample, the first node 104a and second node 104b may comprise the first node 104a and second node 104b described above with reference to FIG. 10.

[0307] At step 1302 a time-bin entanglement process for generating a first photon 108a having quantum entanglement with the first matter qubit 106a is performed at the first node 104a. The entanglement scheme may be a time-bin entanglement scheme. For example, an entanglement scheme having any of the features described above with reference to FIG. 4 and / or FIG. 5A - FIG. 5F may be performed at the first node 104a.

[0308] At step 1304 a time-bin entanglement process for generating a second photon 108b having quantum entanglement with the second matter qubit 106b is performed at the second node 104b. The entanglement scheme may be a time-bin entanglement scheme. For example, an entanglement scheme having any of the features described above with reference to FIG. 4 and / or FIG. 5A - FIG. 5F may be performed at the second node 104b.

[0309] In embodiments, steps 1302 and 1304 are performed in parallel with each other (e.g., substantially simultaneously).

[0310] At step 1306 the first photon 108a and the second photon 108b are directed to input ports 1 110 of an optical coupler 1102 comprising a plurality of input ports 11 10 and a plurality of output ports 11 12. The optical coupler 1102 may comprise an optical coupler 1 102 as described above with reference to FIG. 11. Directing the first photon 108a and the second photon 108b to the input ports 1 110 of the optical coupler 1102 may comprise coupling the photons into photonic links 112 so as to be transported to a measurement system 110 comprising the optical coupler 1102.

[0311] As was explained above, the time-bin entanglement processes performed at the first node 104a and the time-bin entanglement process performed at the second node 104b are performed so as to generate the first photon 108a and the second photon 108b to arrive at input ports 1 110 of the optical coupler 1102 both in a superposition of an early time bin and a late time bin.

[0312] At step 1308 photons are detected at single photon detectors 1 104, 1 106, which are arranged to detect photons output from an output port 1 1 12 of the plurality of output ports 1 1 12 of the optical coupler 1 102. The single photon detectors may comprise the first detector 1 104 and the second detector 1106 as described above with reference to FIG. 11 . As was described above, the detectors 1104, 1106 are configured to detect photons in a first time bin (an early time bin) and a second time bin (a late time bin).

[0313] At step 1310 it is determined whether a photon is detected at any of the detectors 1 104, 1106 in the first (early) time bin. The determination may, for example, be made by the controller 1108 included in the measurement system 1 10 described above with reference to FIG. 11 . As was explained above with reference to FIG. 12 the only measurement outcomes which may correspond to the successful establishment of an entanglement link between thefirst matter qubit 106a and the second matter qubit 106b may be those grouped into the third subset 1214 and fourth subset 1216 of measurement outcomes in the chart 1204 shown in FIG. 12. These measurement outcomes (those grouped in the third subset 1214 and fourth subset 1216) each have in common that a photon is detected at one of the first detector 1 104 or the second detector 1106 in the early (first) time bin. In contrast, at least some of the measurement outcomes grouped in the first subset 1210 and second subset 1212 shown in FIG. 12 do not include a photon being detected in the early (first) time bin. Furthermore, whilst other forms of Bell state measurement of time-bin entangled photons may be performed it has been found more generally that both the ?F+Bell state and the(which may correspond to the generation of useful entanglement links) will include a photon in the early time bin and a photon in the late time bin.

[0314] It has therefore been realised that it can be determined after measurement in the early time bin whether or not the current entanglement link generation attempt has a chance of being successful or if it will be unsuccessful regardless of the results of any measurements in the late time bin. In particular, if no photon is detected at either detector 1 104, 1 106 in the early time bin then it may be determined that the current entanglement link generation attempt will not be successful. If no photon is detected at either detector 1 104, 1106 in the early time bin then this may be because one of the measurement outcomes in the first subset 1210 or second subset 1212, which do not include a photon in the early time bin, will occur. Alternatively, it may be that photon generation at one or both of the first node 104a and the second node 104b failed and / or that one or more generated photons were lost in transport or detection. In any of these scenarios it may be determined that an entanglement link between qubits will not be successfully generated in the current attempt.

[0315] In some examples it may further be determined that an entanglement link between qubits will not be successfully generated in the current attempt if a plurality of photons are detected in the early time bin. For example, it may be determined that an entanglement link between qubits will not be successfully generated in the current attempt if photons are detected at a plurality of detectors (e.g., at both the first detector 1 104 and the second detector 1 106) in the early time bin . Such a scenario could correspond to one of the measurement outcomes in the first subset 1210 of measurement outcomes which may indicate that distinguishable photons have been generated (since according to the Hong-Ou- Mandel effect such a measurement outcome should not occur for indistinguishable photons) and / or may indicate detector noise or a false photon detection. In any of these scenarios it may be determined that an entanglement link between qubits will not be successfully generated in the current attempt.

[0316] In some examples it may further be determined that an entanglement link between qubits will not be successfully generated in the current attempt if two photons are detected at the same detector 1104, 1106 in the early time bin. Such a scenario could correspond toone of the measurement outcomes in the second subset 1212 of measurement outcomes (which may not lead to a useful entanglement link) .

[0317] In contrast, if a photon is detected at either of the detectors 1104, 1106 in the early time bin then it may be determined that the current attempt of entanglement link generation may still lead to a successful entanglement link generation (depending on a measurement outcome in the late time bin). For example, if a photon is detected by only one of the detectors 1 104, 1 106 in the early time bin then it may be determined that a successful entanglement link generation may still occur. In some examples, it may be determined that a successful entanglement link generation may still occur if only a single photon is detected (by one of the detectors 1 104, 1106) in the early time bin.

[0318] At step 1312 of the method 1300 of FIG. 13 the time-bin entanglement process at the first node 104a and the second node 104b is restarted if no photons are detected at any of the detectors 1 104, 1106 in the early time bin. In some examples, the time-bin entanglement process at the first node 104a and the second node 104b may also be restarted if a plurality of photons are detected in the early time bin. For example, detecting a photon at both detectors 1104, 1106 in the early time bin and / or detecting two photons at a single detector 1 104, 1106 in the early time bin may lead to restarting the time-bin entanglement process.

[0319] Restarting the time-bin entanglement process at the first node 104a and the second node 104b may comprise generating and / or transmitting a control signal (e.g., from a controller 1108 included in or coupled to a measurement system 1 10). For example, a control signal may be transmitted to a controller 1004 configured to control entanglement scheme processes performed at the first node 104a and / or second node 104b. Additionally or alternatively, a control signal may be transmitted to an interaction means 208 at the first node 104a and / or the second node 104b. A control signal may cause an appropriate component (such as controller 1004) to restart a time-bin entanglement process or scheme.

[0320] In some examples, an electronic display may display an output from the quantum communication system 1002. The electronic display may take the form of the display forming part of the electronic device 1602 described below in relation to the embodiment of Figure 16 or may take any other suitable form.

[0321] In some examples, the electronic display may display a result from step 1310 and / or from step 1312. In other words, the electronic display may display the detection result from step 1310 and / or may display a notification relating to the restarting of the time-bin entanglement process.

[0322] In some examples, the electronic display may display an output based on the control signal transmitted to the controller 1004. In some examples, the controller 1004 may formpart of the electronic device 1602 and the electronic display may be a display associated therewith.

[0323] In some examples, the electronic display may display output data in relation to one or more attempts at generation of quantum entanglement. For example, the electronic display may display a percentage or absolute value of the number of successful and / or failed (i.e. restarted) attempts.

[0324] In some examples, the electronic display may display an output which is not concurrent with the current state of the quantum communication system 1002 and may display an output representing data relating to a previous time period or a summary of the output data in relation to one or more attempts at generation of quantum entanglement. For example, the electronic display may display a percentage or absolute value of the number of successful and / or failed (i.e. restarted) attempts as a function of time over a predetermined time period. In embodiments, the predetermined time period may be of the order of 1 hour to 24 hours.

[0325] In some examples, an output from the quantum communication system 1002 may be provided via different means from the electronic display. For example, a log or other data recordal of the output from the quantum communication system 1002 may be provided. The log or data recordal may be in the form of a log file or other data file. Alternatively, the log or data recordal may be provided as a data stream to be monitored or recorded by other elements of the system (not shown). The log may comprise data relating to a percentage or absolute value of the number of successful and / or failed (i.e. restarted) attempts as a function of time over a predetermined time period.

[0326] Restarting an entanglement generation process or scheme may comprise restarting the process or scheme before a process associated with photon emission in a late time bin is performed. For example, an entanglement scheme as described above with reference to FIG. 4 and FIG. 5A - FIG. 5F may be restarted before a second instance of an excitation field (corresponding to stimulating photon emission in the late time bin). Restarting an entanglement process or scheme may comprise returning the first matter qubit 106a and the second matter qubit 106b to an original superposition state (e.g., the state depicted in FIG. 5B) and performing a process associated with photon emission in an early time bin. For example, restarting an entanglement process or scheme as described above may comprise returning at least to step 404 of the method 400 of FIG. 4 and proceeding with the remainder of the method 400 .

[0327] Restarting an entanglement generation process or scheme as described above may significantly reduce a time taken to perform an unsuccessful attempt at entanglement link generation. For example, merely to provide illustrative examples, in some examples a total entanglement link generation process may take approximately 2000-3000 ns to perform. Byapplying a method 1300 as described above with reference to FIG. 13, a time taken to perform an unsuccessful entanglement link generation (e.g., by restarting the process based on measurements in the early time bin) may be approximately halved or more. For example, a time taken to perform an unsuccessful entanglement link generation process may be reduced to about 1000 ns .

[0328] In at least some examples, a majority of entanglement link generation attempts may result in no photon being detected in the early time bin (for example, due to failed photon generation, photon loss or any of the other scenarios described above). By applying a method 1300 as described above with reference to FIG. 13 a majority of entanglement link generation processes may therefore be restarted based on measurements made in the early time bin. In this way a rate at which entanglement link generation attempts are performed may be significantly increased (for example, such a rate may be up to doubled). Increasing a rate at which entanglement link generation attempts are performed will serve to increase a rate R at which entanglement links can be successfully generated even where most attempts are not successful.

[0329] As was explained above with reference to FIG. 13, in some situations an entanglement generation scheme may not proceed to completion. For example, it may be determined after steps associated with generating a photon 210 in an early time bin that the scheme will not lead to successful generation of an entanglement link and the scheme may be truncated and / or restarted.

[0330] FIG. 14 is a flowchart of a method 1400 which may be performed at a node 204 of a quantum communication system 1002. The node 204 may, for example, comprise the first node 104a or the second node 104b described above. At step 1402 a matter qubit 206 is arranged in a resonant optical cavity 202. Step 1402 of the method 1400 of FIG. 14 corresponds to step 402 of the method 400 of FIG. 4. Any of the features described above in connection with step 402 may also apply to step 1402 and no detailed description will be provided again with reference to FIG. 14.

[0331] At step 1404 the matter qubit 206 is initialised in a superposition of a first ground state energy level 302 and a second ground state energy level 304 . Step 1404 of the method 1400 of FIG. 14 corresponds to step 404 of the method 400 of FIG. 4. Any of the features described above in connection with step 404 may also apply to step 1404 and no detailed description will be provided again with reference to FIG. 14.

[0332] At step 1406 the matter qubit 206 is exposed to an excitation field configured to excite the matter qubit 206 from the second ground state energy level 304 to an excited state energy level 306. Step 1406 of the method 1400 of FIG. 14 corresponds to step 406 of the method 400 of FIG. 4. Any of the features described above in connection with step 406 mayalso apply to step 1406 and no detailed description will be provided again with reference to FIG. 14.

[0333] At step 1408 it is determined whether a control signal is received to restart the entanglement generation process. As was described above, a control signal to restart an entanglement generation process may be transmitted if no photon is detected by any detector 1 104, 1 106 of a measurement system 110 in an early time bin. Additionally or alternatively, a control signal to restart an entanglement generation process may be transmitted if a plurality of photons is detected in an early time bin. For example, if a photon is detected by two detectors 1 104, 1106 in the early time bin and / or two photons are detected by one of the detectors 1104, 1106 in the early time bin then a control signal may be transmitted to restart the time-bin entanglement process.

[0334] If a control signal is received to restart the time-bin entanglement process (or equivalently no control signal to proceed with the time-bin entanglement process is received) then the method 1400 returns to step 1404 and proceeds from step 1404. If no control signal is received to restart the time-bin entanglement process (or equivalently a control signal to proceed with the time-bin entanglement process is received) then the method 1400 proceeds to step 1410.

[0335] At step 1410 the matter qubit 206 is subjected to a control field configured to cause an energy level transition from the first ground state energy level 302 to the second ground state energy level 304. Step 1410 of the method 1400 of FIG. 14 corresponds to step 408 of the method 400 of FIG. 4. Any of the features described above in connection with step 408 may also apply to step 1410 and no detailed description will be provided again with reference to FIG. 14.

[0336] At step 1412 the matter qubit 206 is exposed to a second instance of the excitation field. Step 1412 of the method 1400 of FIG. 14 corresponds to step 410 of the method 400 of FIG. 4. Any of the features described above in connection with step 410 may also apply to step 1412 and no detailed description will be provided again with reference to FIG. 14.

[0337] In the method 1400 of FIG. 14, the time-bin entanglement process may be restarted after step 1406. Additionally or alternatively, the time-bin entanglement process may be restarted after step 1410 of the method 1400. For example, the method 1400 may proceed to step 1410 to apply a control field before restarting and returning, for example, to step 1404.

[0338] As has been demonstrated with reference to FIG. 14, not every instance of a method of generating a photon having quantum entanglement with a matter qubit 206 may proceed to a second instance of an excitation field associated with a late time bin photon emission. For example, a method which only includes steps 402, 404 and 406 (equivalently step 1402,1404 and 1406) may still have utility in its own right since useful information can be attained from these steps alone which may determine one or more further steps to be performed.

[0339] In some examples, an electronic display may display an output from the quantum communication system 1002. The electronic display may take the form of the display forming part of the electronic device 1602 described below in relation to the embodiment of Figure 16 or may take any other suitable form.

[0340] In some examples, the electronic display may display a result from step 1408 and / or any other suitable step. In other words, the electronic display may display the detection result from step 1310 and / or may display a notification relating to the restarting of the time-bin entanglement process.

[0341] In some examples, the electronic display may display an output based on the control signal transmitted to the controller 1004. In some examples, the controller 1004 may form part of the electronic device 1602 and the electronic display may be a display associated therewith.

[0342] In some examples, the electronic display may display output data in relation to one or more attempts at generation of quantum entanglement. For example, the electronic display may display a percentage or absolute value of the number of successful and / or failed (i.e. restarted) attempts .

[0343] In some examples, the electronic display may display an output which is not concurrent with the current state of the quantum communication system 1002 and may display an output representing data relating to a previous time period or a summary of the output data in relation to one or more attempts at generation of quantum entanglement. For example, the electronic display may display a percentage or absolute value of the number of successful and / or failed (i.e. restarted) attempts as a function of time over a predetermined time period. In embodiments, the predetermined time period may be of the order of 1 hour to 24 hours.

[0344] In some examples, an output from the quantum communication system 1002 may be provided via different means from the electronic display. For example, a log or other data recordal of the output from the quantum communication system 1002 may be provided. The log or data recordal may be in the form of a log file or other data file. Alternatively, the log or data recordal may be provided as a data stream to be monitored or recorded by other elements of the system (not shown). The log may comprise data relating to a percentage or absolute value of the number of successful and / or failed (i.e. restarted) attempts as a function of time over a predetermined time period.

[0345] It has been further realised that during repeated attempts of generating entanglement links, at least some measurement outcomes may provide information related to changes over time in the distinguishability of generated photons 108a, 108b. FIG. 15 is aflowchart of a method 1500 of monitoring a system for generating entanglement between a first matter qubit 106a disposed at a first node 104a and a second matter qubit 106b disposed at a second node 104b. The method 1300 may be performed in a quantum communication system 1002 as described herein. For example, the first node 104a and second node 104b may comprise the first node 104a and second node 104b described above with reference to FIG. 10.

[0346] At step 1502 a time-bin entanglement process for generating a first photon 108a having quantum entanglement with the first matter qubit 106a is repeatedly performed at the first node 104a. For example, an entanglement scheme having any of the features described above with reference to FIG. 4 and / or FIG. 5A - FIG. 5F may be repeatedly performed at the first node 104a.

[0347] At step 1504 a time-bin entanglement process for generating a second photon 108b having quantum entanglement with the second matter qubit 106b is repeatedly performed at the second node 104b. For example, an entanglement scheme having any of the features described above with reference to FIG. 4 and / or FIG. 5A - FIG. 5F may be repeatedly performed at the second node 104b.

[0348] Steps 1502 and 1504 may be performed in parallel with each other. For example, each time-bin entanglement process which is performed at the first node 104a may be performed in parallel (e.g., substantially simultaneously) with a corresponding time-bin entanglement process at the second node 104b.

[0349] At step 1506 the first photon 108a and the second photon 108b are directed to input ports 1 110 of an optical coupler 1102 comprising a plurality of input ports 11 10 and a plurality of output ports 11 12. Step 1506 of the method 1500 of FIG. 15 may correspond with step 1306 of the method 1300 of FIG. 13. Any of the features described above with reference to step 1306 of the method 1300 of FIG. 13 may also apply to step 1506 of the method 1500 of FIG. 15. For example, the optical coupler 1102 may comprise an optical coupler 1102 as described above with reference to FIG. 11. Directing the first photon 108a and the second photon 108b to the input ports 1 110 of the optical coupler 1102 may comprise coupling the photons into photonic links 112 so as to be transported to a measurement system 110 comprising the optical coupler 1102.

[0350] Step 1506 may be performed for each repetition of the time-bin entanglement processes performed at the first node 104a and the second node 104b. That is, for each time-bin entanglement process performed at the first node 104a and the second node 104b any generated photons are directed to input ports 1 110 of an optical coupler 1 102. As was explained above, the time-bin entanglement processes performed at the first node 104a and the time-bin entanglement process performed at the second node 104b are performed so asto generate the first photon 108a and the second photon 108b to arrive at input ports 11 10 of the optical coupler 1 102 both in a superposition of an early time bin and a late time bin.

[0351] At step 1508 photons are detected at single photon detectors 1 104, 1 106, which are arranged to detect photons output from an output port 1 1 12 of the plurality of output ports 1 1 12 of the optical coupler 1 102. The single photon detectors may comprise the first detector 1 104 and the second detector 1106 as described above with reference to FIG. 11 . As was described above, the detectors 1104, 1106 are configured to detect photons in a first time bin (an early time bin) and a second time bin (a late time bin) .

[0352] Step 1508 may be performed for each repetition of the time-bin entanglement processes performed at the first node 104a and the second node 104b, that is, for each timebin entanglement process performed at the first node 104a and the second node 104b, the detectors 1104, 1106 may be configured to detect photons output from output ports 1 112 of the optical coupler 1 102. Any photon detections may be performed in at least a first (early) time bin and may be performed in a second (late) time bin if the time-bin entanglement processes proceed to the second (late) time bin (e.g., are not restarted after measurement in the early time bin as described above with reference to the method 1310 of FIG. 13).

[0353] At step 1510 a rate at which photons are detected by different single photon detectors and in the same time bin is determined. The rate is determined over a plurality of repetitions of the time-bin entanglement processes performed at the first node and the second node. The determined rate may, for example, comprise a number of detections by different detectors in the same time bin detected per unit of time. Alternatively the determined rate may comprise a number of detections by different detectors in the same time bin detected per number of time-bin entanglement processes performed.

[0354] Detections of two photons at different detectors 1 104, 1 106 in the same time-bin correspond with the measurement outcomes grouped in the first subset 1210 in the chart 1204 of FIG. 12. As was described above, for two indistinguishable photons, the photons should group together and exit the same output port 1 1 12 according to the Hong-Ou-Mandel effect. Instances of detecting two photons at different detectors 1 104, 1 106 and in the same time-bin may therefore be taken to be an indication that the photons are distinguishable (i.e. , not indistinguishable). However, instances of detecting two photons at different detectors 1 104, 1 106 and in the same time-bin may also result from other effects such as detector noise and / or false detection events.

[0355] A rate of detector noise and / or false detection events causing instances of detecting two photons at different detectors 1104, 1106 and in the same time-bin may remain relatively stable over time. Changes in the rate of detection of instances of detecting two photons at different detectors 1 104, 1 106 and in the same time-bin may therefore be considered to be indicative to changes in the distinguishability of photons generated using the time-binentanglement generation processes. For example, an increase in the rate of detection of instances of detecting two photons at different detectors 1 104, 1106 and in the same timebin, may be an indication that photons generated by the time-bin entanglement generation process are no longer indistinguishable. For example, one or more parameters such as frequency, timing, and / or polarisation of one or both of the time-bin entanglement generation processes performed at the first node 104a and the second node 104b may drift over time causing generated photons to become distinguishable.

[0356] Determining and monitoring a rate at which photons are detected by different detectors 1104, 1 106 and in the same time bin may provide an indication of any changes in the distinguishability of generated photons over time. Such changes may, for example, be used to diagnose and correct for any problems in a quantum communication system 1002 .

[0357] In some examples, an electronic display may display an output from the quantum communication system 1002. The electronic display may take the form of the display forming part of the electronic device 1602 described below in relation to the embodiment of Figure 16 or may take any other suitable form.

[0358] In some examples, the electronic display may display an output parameter from step 1510 and / or any other suitable step. In other words, the electronic display may display a rate determined in step 1510. The rate may be a current rate or an averaged rate, or any suitable rate measured over a timeframe that enables a user to identify the determined rate and, if necessary, diagnose and correct for any problems in the quantum communication system 1002.

[0359] In some examples, the electronic display may display an output which is not concurrent with the current state of the quantum communication system 1002 and may display an output representing data relating to a previous time period or a summary or average of the rate over a period of time. For example, the electronic display may display an average rate as a function of time over a predetermined time period. In embodiments, the predetermined time period may be of the order of 1 hour to 24 hours.

[0360] In some examples, an output from the quantum communication system 1002 may be provided via different means from the electronic display. For example, a log or other data recordal of the output from the quantum communication system 1002 may be provided. The log or data recordal may be in the form of a log file or other data file. Alternatively, the log or data recordal may be provided as a data stream to be monitored or recorded by other elements of the system (not shown).

[0361] It is further noted that a controller may be provided for performing step 1510. In other words, the controller may be configured to: receive data from the single photon detectors indicative of measurements of photons made by the single photon detectors; and determine a rate at which photons are detected by different single photon detectors and in the sametime bin. Thus, the controller may be separate from the remainder of the system and receive data from the single photon detectors which can then, in embodiments, be displayed on an electronic display or stored in a log as described above.

[0362] Several examples have been described herein in the context of generating quantum entanglement links between matter qubits 106a, 106b disposed at two nodes 104a, 104b. in some examples, a quantum communication system may comprise more than two nodes. In such a system any of the nodes may include any of the features described herein in the context of a two node system. Furthermore, any of the methods described herein may be performed for any node and / or combination of nodes in a multi-node system. For example, an entanglement scheme as described above with reference to FIG. 4 and FIG. 5A - FIG. 5F may be performed at any node of a multi-node system and may be performed at any two nodes in parallel.

[0363] For a quantum communication system comprising more than two nodes it may be desirable to be able to generate entanglement links between any two of the nodes. For example, in a four node system it may be desirable to generate entanglement links between one or more of: a first node and a second node, the first node and a third node, the first node and a fourth node, the second node and the third node, the second node and the fourth node and / or the third node and the fourth node. This may be achieved, for example, by successively performing entanglement generation schemes in parallel at two of the nodes between which an entanglement link is to be generated. The system may include one central measurement system 110 which is arranged to perform Bell state measurements of any photon pair arriving from any two nodes. An optical switching network may be provided in order to direct photons generated at any two nodes to input ports 11 10 of an optical coupler 1 102 included in the measurement system 110. In other examples (e.g., in larger systems with more nodes) a plurality of measurement systems 1 10 may be provided in order to be able to perform a plurality of Bell state measurements in parallel and generate a plurality of entanglement links in parallel.

[0364] Examples have been described herein in the context of nodes of a quantum communication system where a matter qubit is disposed at each node. It will be appreciated, however, that in practice there may be a plurality of matter qubits disposed at one or more of the nodes. For example, there may be a plurality of matter qubits disposed at each node. At least one of the matter qubits at a node may be used to establish an entanglement link with another node as described herein. Other matter qubits at the node may be used for other purposes such as to perform local compute operations. In some examples, a plurality of matter qubits at a node may be used to generate a plurality of entanglement links. For example, in a four node system, a first matter qubit at a first node may be used to generate an entanglement link with a second node, a second matter qubit at the first node may beused to generate an entanglement link with a third node and / or a fourth matter qubit at the first node may be used to generate an entanglement link with a fourth node.

[0365] In some examples, a plurality of entanglement links may be generated between two nodes. For example, a first matter qubit disposed at a first node may be entangled with a second qubit disposed at a second node and a third matter qubit disposed at the first node may be entangled with a fourth matter qubit disposed at the second node.

[0366] The methods and apparatus disclosed herein may be used to generate any number of entanglement links between any number of nodes and utilising any number of matter qubits

[0367] Various methods have been described herein in which some of the method steps may be implemented on any suitable electronic device (such as a controller) and / or combination of electronic devices (e.g., controllers). Furthermore, example apparatus have been described herein comprising one or more controllers which may be embodied as one or more electronic devices (e.g., computing devices). For example, the controller 1004 forming part of the quantum communication system 1002 shown in FIG. 10 and / or the controller 1 108 forming part of the measurement system 110 shown in FIG. 11 may be embodied as one or more electronic devices (e.g., computing devices). The electronic devices, computing devices and / or controllers described herein may comprise one or more classical computing devices.

[0368] FIG. 16 is a schematic illustration of an example electronic device 1602, which may be used to realise one or more of the controllers described herein. The electronic device 1602 may include at least one processing unit 1604, memory 1608 and an input / output interface 1606. The processing unit 1604 may include any suitable processer and / or combination of processors. For example, the processing unit 1604 may include one or more of a Central Processing Unit (CPU) and a Graphical Processing Unit (GPU). The memory 1608 may include volatile memory and / or non-volatile / persistent memory. The memory 1608 may, for example, be used to store data such as an operating system, instructions to be executed by the processing unit (e.g. in the form of software to be executed by the processing unit), configuration information related to the electronic device 1602, and / or configuration information associated with any other device, node or module in a quantum communication system. In some examples, the memory 1608 may be used to store instructions for executing any of the methods disclosed herein. In some examples, the memory 1608 may be used to store a register of entangled matter qubits 206 and / or entanglement links which have been generated in a quantum communication system.

[0369] At least the processing unit 1604 is connected to the input / output interface 1606. The input / output interface 1606 may facilitate communication with one or more other devices. For example, the input / output interface 1606 may be operable to transmit and / or receivecommunications to / from other devices in the multi-core quantum computing system and / or one or more devices outside of the multi-core quantum computing system.

[0370] Optionally, the electronic device 1602 may further include a display (not shown). The display may comprise any suitable electronic display . The display may be connected at least to the processing unit 1604. The processing unit 1604 may generate display signals which are sent to the display in order to cause the display information.

[0371] Features, integers, characteristics or groups described in conjunction with a particular aspect, embodiment or example of the invention are to be understood to be applicable to any other aspect, embodiment or example described herein unless incompatible therewith. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and / or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and / or steps are mutually exclusive. The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed. In particular, any dependent claims may be combined with any of the independent claims and any of the other dependent claims.

[0372] Each feature disclosed in this specification (including any accompanying claims, abstract and drawings), may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features. The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed. The claims should not be construed to cover merely the foregoing embodiments, but also any embodiments which fall within the scope of the claims.

Claims

CLAIMS1 . A method for attempting generation of quantum entanglement between a first matter qubit disposed at a first node and a second matter qubit disposed at a second node, wherein the method comprises: performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit; performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit; directing the first photon and the second photon to input ports of an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the time-bin entanglement processes performed at the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; detecting photons at single photon detectors each arranged to detect photons output from an output port of the plurality of output ports of the optical coupler in the first time bin and in the second time bin; determining whether a photon is detected at any of the single photon detectors in the first time bin; and if no photons are detected at any of the single photon detectors in the first time bin, restarting the time-bin entanglement process at the first node and the second node.

2. A method for attempting generation of quantum entanglement between a first matter qubit disposed at a first node and a second matter qubit disposed at a second node, wherein the method comprises: performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit; performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit; directing the first photon and the second photon to input ports of an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the time-bin entanglement processes performed at the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin;detecting photons at single photon detectors each arranged to detect photons output from an output port of the plurality of output ports of the optical coupler in the first time bin and in the second time bin; determining whether a plurality of photons are detected at the single photon detectors in the first time bin; and if a plurality of photons are detected at the single photon detectors in the first time bin, restarting the time-bin entanglement process at the first node and the second node.

3. The method for attempting generation of claim 2, wherein determining whether a plurality of photons are detected at the single photon detectors in the first time bin comprises determining whether a plurality of photons are detected by one of the single photon detectors in the first time bin.

4. The method for attempting generation of claim 2 or 3, wherein determining whether a plurality of photons are detected at the single photon detectors in the first time bin comprises determining whether photons are detected by a plurality of single photon detectors in the first time bin.

5. The method for attempting generation of any one of the preceding claims, wherein restarting the time-bin entanglement process at the first node and the second node comprises transmitting a control signal for restarting the time-bin entanglement process at the first node and the second node.

6. The method for attempting generation of claim 5, wherein the control signal is transmitted from a first controller forming part of a measurement system.

7. The method for attempting generation of claim 5 or 6, wherein the control signal is transmitted to a second controller configured to control entanglement scheme processes at the first node and / or second node.

8. The method for attempting generation of claim 7, wherein the first and / or second controller forms part of an electronic device.

9. The method for attempting generation of claim 8, wherein the method further comprises displaying information on an electronic display of the electronic device.

10. The method for attempting generation of any one of the preceding claims, further comprises displaying information on an electronic display.1 1 . The method for attempting generation of claim 10, wherein the information comprises a detection result and / or a notification relating to the restarting of the time-bin entanglement process.

12. The method for attempting generation of claim 10, wherein the information comprises information relating to one or more attempts at generation of quantum entanglement.

13. The method of claim 1 1 or 12, wherein the information comprises a percentage or absolute value of the number of successful and / or failed attempts at generation of quantum entanglement.

14. The method for attempting generation of claim 1 1 , 12 or 13, wherein the electronic display displays the information as a function of time over a predetermined time period.

15. The method for attempting generation of any one of the preceding claims, further comprising the step of: outputting information relating to one or more attempts at generation of quantum entanglement.

16. The method for attempting generation of claim 15, wherein the step of outputting information relating to one or more attempts at generation of quantum entanglement comprises: entering the information into a log file.

17. The method for attempting generation of claim 16, wherein the method further comprises: storing the log file.

18. The method for attempting generation of any one of claims 15 to 17, wherein the information comprises a detection result and / or a notification relating to the restarting of the time-bin entanglement process.

19. The method for attempting generation of claim 18, wherein the information comprises a percentage or absolute value of the number of successful and / or failed attempts at generation of quantum entanglement.

20. The method for attempting generation of any one of the preceding claims, wherein the performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit comprises: exposing the first matter qubit to a first instance of an excitation field for exciting the first matter qubit to an excited state energy level, the first instance of the excitation field being associated with emission of the first photon in the first time bin; andexposing the first matter qubit to a second instance of the excitation field for exciting the first matter qubit to the excited state energy level, the second instance of the excitation field being associated with emission of the first photon in the second time bin, wherein restarting the time-bin entanglement process at the first node comprises restarting the time-bin entanglement process before exposing the first matter qubit to the second instance of the excitation field.

21. The method for attempting generation of any one of the preceding claims, wherein the performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit comprises: exposing the second matter qubit to a second instance of an excitation field for exciting the second matter qubit to an excited state energy level, the first instance of the excitation field being associated with emission of the second photon in the first time bin; and exposing the second matter qubit to a second instance of the excitation field for exciting the second matter qubit to the excited state energy level, the second instance of the excitation field being associated with emission of the second photon in the second time bin, wherein restarting the time-bin entanglement process at the second node comprises restarting the time-bin entanglement process before exposing the second matter qubit to the second instance of the excitation field.

22. The method for attempting generation of any one of the preceding claims, wherein one or both of: performing, at the first node, a time-bin entanglement process for generating a first photon having quantum entanglement with the first matter qubit; and performing, at the second node, a time-bin entanglement process for generating a second photon having quantum entanglement with the second matter qubit comprises the steps of: arranging the matter qubit in a resonant optical cavity configured to stimulate emission of a photon from the matter qubit when the matter qubit is arranged in the cavity and in an excited state energy level (e), emission of the photon from the matter qubit causing the matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); initialising the matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); exposing the matter qubit to a first instance of an excitation field configured to excite the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e);subjecting the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and exposing the matter qubit to a second instance of the excitation field.

23. The method for attempting generation of claim 22, wherein, prior to the step of arranging the matter qubit in a resonant optical cavity, the method comprises: selecting a matter qubit having energy levels such that the probability of emission of a photon from the matter qubit and the matter qubit transitioning from an excited state energy level (e) to a third ground state energy level (GS3) is greater than the probability of the matter qubit transitioning from an excited state energy level (E) to a second ground state energy level (GS2).

24. The method for attempting generation of claim 22 or 23, wherein restarting the time-bin entanglement process at the first node and / or the second node comprises restarting the timebin entanglement process before exposing the first and / or second matter qubit to the second instance of the excitation field.

25. A system for generating quantum entanglement between a first matter qubit and a second matter qubit, wherein the system comprises: a first node for generating a first photon having quantum entanglement with the first matter qubit using a time-bin entanglement process; a second node for generating a second photon having quantum entanglement with the second matter qubit using a time-bin entanglement process; an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the optical coupler is arranged to receive photons emitted from the first node at a first of the plurality of input ports and photons emitted from the second node at a second of the plurality of input ports, wherein the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; a plurality of single photon detectors each arranged to detect photons output from an output port of the plurality of output ports in the first time bin and in the second time bin; and a controller configured to: receive data from the single photon detectors indicative of measurements of photons made by the single photon detectors;determine whether a photon is detected at any of the single photon detectors in the first time bin; and if no photons are detected at any of the single photon detectors in the first time bin, to transmit a control signal for restarting the time-bin entanglement process.

26. A system for generating quantum entanglement between a first matter qubit and a second matter qubit, wherein the system comprises: a first node for generating a first photon having quantum entanglement with the first matter qubit using a time-bin entanglement process; a second node for generating a second photon having quantum entanglement with the second matter qubit using a time-bin entanglement process; an optical coupler comprising a plurality of input ports and a plurality of output ports, wherein the optical coupler is arranged to receive photons emitted from the first node at a first of the plurality of input ports and photons emitted from the second node at a second of the plurality of input ports, wherein the first node and the second node are configured to generate the first photon and the second photon to arrive at input ports of the optical coupler both in a superposition of a first time bin and a second time bin; a plurality of single photon detectors each arranged to detect photons output from an output port of the plurality of output ports in the first time bin and in the second time bin; and a controller configured to: receive data from the single photon detectors indicative of measurements of photons made by the single photon detectors; determine whether a plurality of photons are detected at the single photon detectors in the first time bin; and if a plurality of photons are detected at the single photon detectors in the first time bin, to transmit a control signal for restarting the time-bin entanglement process.

27. The system of claim 26, wherein the controller is further configured to determine whether a plurality of photons are detected at the single photon detectors in the first time bin by determining whether a plurality of photons are detected by one of the single photon detectors in the first time bin.

28. The system of claim 26 or 27, wherein the controller is further configured to determine whether a plurality of photons are detected at the single photon detectors in the first time bin by determining whether photons are detected by a plurality of single photon detectors in the first time bin.

29. The system of any one of claim 25 to 28, further comprising a second controller operable to receive the transmitted control signal, the second controller being configured to control entanglement scheme processes at the first node and / or second node.

30. The system of claim 29, further comprising an electronic device and wherein the controller and / or second controller forms part of an electronic device.

31. The system of claim 30, wherein the electronic device further comprises an electronic display configured to display information.

32. The system of claim 31 , wherein the electronic device and / or electronic display is configured to display a detection result and / or a notification relating to the restarting of the time-bin entanglement process.

33. The system of claim 31 or 32, wherein the electronic display is configured to display information relating to one or more attempts at generation of quantum entanglement.

34. The system of claim 33, wherein the electronic display is configured to display a percentage or absolute value of the number of successful and / or failed attempts at generation of quantum entanglement.

35. The system of any one of claims 31 to 34, wherein the electronic display is configured to display the information as a function of time over a predetermined time period.

36. The system of any one of claims 25 to 35, further configured to output information relating to one or more attempts at generation of quantum entanglement.

37. The system of claim 36, further configured to enter the information into a log file.

38. The system of claim 37, further configured to store the log file.

39. The system of claim 36 to 38, wherein the information comprises a detection result and / or a notification relating to the restarting of the time-bin entanglement process.

40. The system of claim 36 to 39, wherein the information comprises a percentage or absolute value of the number of successful and / or failed attempts at generation of quantum entanglement.

41. The system of any one of claims 25 to 40, wherein the first node for generating a first photon having quantum entanglement with the first matter qubit comprises: a first resonant optical cavity for receiving a first matter qubit, wherein the first optical cavity is configured to stimulate emission of a photon from the first matter qubit when the firstmatter qubit is arranged in the optical cavity in an excited state energy level (e), emission of the photon from the first matter qubit causing the first matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); an interaction means configured to: initialise the first matter qubit in a superposition of a first ground state energy level (GS1 ) and a second ground state energy level (GS2); expose the first matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e); subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field.

42. The system of claim 41 , further comprising: a first matter qubit having energy levels selected such that the probability of emission of a photon from the first matter qubit and the first matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3) is greater than the probability of the first matter qubit transitioning from the excited state energy level (E) to the second ground state energy level (GS2).

43. The system of any one of claims 25 to 42, wherein the second node for generating a second photon having quantum entanglement with the second matter qubit comprises: a second resonant optical cavity for receiving a second matter qubit, wherein the second optical cavity is configured to stimulate emission of a photon from the second matter qubit when the second matter qubit is arranged in the optical cavity in an excited state energy level (e), emission of the photon from the second matter qubit causing the second matter qubit to transition from the excited state energy level (e) to a third ground state energy level (GS3); an interaction means configured to: initialise the second matter qubit in a superposition of a first ground state energy level (GS1 ) and the second ground state energy level (GS2); expose the second matter qubit to a first instance of an excitation field for exciting the matter qubit from the second ground state energy level (GS2) to the excited state energy level (e);subject the matter qubit to a control field configured to cause an energy level transition from the first ground state energy level (GS1 ) to the second ground state energy level (GS2); and expose the matter qubit to a second instance of the excitation field,44. The system of claim 43, further comprising: a second matter qubit having energy levels selected such that the probability of emission of a photon from the second matter qubit and the second matter qubit transitioning from the excited state energy level (e) to the third ground state energy level (GS3) is greater than the probability of the second matter qubit transitioning from the excited state energy level (E) to the second ground state energy level (GS2).

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