Quantum entanglement apparatus

Abstract

A quantum entanglement apparatus comprising: a first interference arrangement configured to receive photons with a first polarisation from a plurality of nodes; and a second interference arrangement configured to receive photons with a second polarisation from the plurality of nodes, wherein each of the first and second interference arrangements comprises: a plurality of inputs, each input configured to receive photons from a respective node of the plurality of nodes; a plurality of outputs; and a network of paths from each input to each output, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs, wherein the first and second interference arrangements are configured such that detection of photons at the outputs of the first and second interference arrangements enables entanglement between at least two nodes of the plurality of nodes.

Description

[0001] QUANTUM ENTANGLEMENT APPARATUS

[0002] The present disclosure relates to apparatus and methods for improved quantum entanglement. In particular, but not exclusively, the present disclosure relates to apparatus and methods for providing compact and scalable quantum entanglement between multiple nodes.

[0003] Remote entanglement between separated memory or processing nodes is a key ingredient for distributed quantum computing, secure quantum communications, remote sensing and other quantum technologies. These nodes can be implemented using a variety of quantum objects, including trapped ions, neutral atoms, defects in diamonds, or doped crystals, among others. Quantum entanglement over separated nodes can be created using the photons emitted by these quantum systems. Optical photons are an appealing candidate, as they can travel long distances in free space, or in optical fibres, with high transmission efficiencies and with negligible loss of coherence.

[0004] A convenient approach to achieve remote entanglement between two separate nodes is to first create a photon-atom entangled pair in each node, capture the photons, and measure them using a photonic Bell state analyser. Whilst such remote entanglement is described with respect to the creation of a photon-“atom” pair, it also works for photon pairs created by the formation of photons entangled with ions, quantum dots, atomic ensembles, nitrogen vacancy (NV) centres or any further entity that can be entangled with a photon.

[0005] A photonic Bell state analyser implements a projective measurement in the photons, resulting in the swapping of entanglement from the initial two photon-atom pairs. After the successful measurement of the photons, this process projects the initially separated atoms into an entangled state, which resembles a Bell state with high accuracy. Photonic Bell state analysers are also the key components of a quantum repeater, which allows for long distances quantum communications.

[0006] The most successful demonstrations of this protocol have used the polarisation degree of freedom of the photons. Following the early proposals, the construction of polarisation Bell state analysers has followed the design shown at Figure 1. Figure 1 shows a schematic representation of standard Bell state analyser 100 of the prior art. The standard Bell state analyser 100 is used to provide quantum entanglement between two nodes 2, 4. In an example, the two nodes 2, 4 are ion traps which are subject to synchronised laser pulses in order to excite ions in each of the two nodes 2, 4. The subsequent decay from the excited states results in the emission of a photon with orthogonal polarisation modes from each of the two nodes 2, 4. The photons from each of the nodes 2, 4 are directed to a non-polarising beam splitter 32, such that horizontal and vertical polarisation modes are directed along an optical pathway 12 from a first node 2 to the beam splitter 32 and horizontal and vertical polarisation modes are directed along an optical pathway 14 from a second node 4 to the beam splitter 32. The beam splitter 32 uses the Hong-Ou-Mandel effect such that if two photons enter simultaneously at two different inputs of beam splitter 32, the two photons exit the beam splitter at the same output of beam splitter 32, with an equal probability of exiting the beam splitter 32 together in either direction. Photons exiting the beam splitter 32 in a first direction are directed along an optical pathway 102 to a first polarising beam splitter 22. Photons exiting the beam splitter 32 in a second direction are directed along an optical pathway 104 to a second polarising beam splitter 24.

[0007] The first and second polarising beam splitters 22, 24 are each configured to direct light in a different direction, based on the polarisation of the light. Accordingly, in the example of Figure 1, horizontally polarised light incident on the first polarising beam splitter 22 is directed by the first polarising beam splitter 22 in a direction along an optical pathway 106 to a first photon detector 40A and vertically polarised light incident on the first polarising beam splitter 22 is directed in a direction along an optical pathway 108 to a second photon detector 40B. Similarly, horizontally vertically polarised light incident on the second polarising beam splitter 24 is directed along an optical pathway 110 by the second polarising beam splitter 24 to a third photon detector 40C and horizontally polarised light incident on the second polarising beam splitter 24 is directed along an optical pathway 112 by the second polarising beam splitter 24 to a fourth photon detector 40D. In the example of Figure 1, the optical pathways 12, 14, 102, 104, 106, 108, 110, 112 can be either free-space or the guided mode of a fibre. The Bell state analyser 100 is implemented in order to take advantage of the Hong-Ou-Mandel effect in the nonpolarising beam splitter 32, the use of polarisation sensitive beam splitters 22, 24, and single photon detectors (SPDs) 40A to 40D. Upon the detection of two photons with orthogonal polarisation in two different single photon detectors of the photon detectors 40A to 40D, it can be declared that entanglement was created between the two atoms of the nodes 2, 4.

[0008] Whilst the Bell state analyser 100 shown in Figure 1 enables quantum entanglement between two nodes 2, 4, implementation of such Bell state analysers with free-space optics uses bulky optical components, which may be difficult to keep stable and which require careful alignment. Such arrangements are therefore difficult to realise, unsuitable for scaling applications and result in practical limitations. Further, such Bell state analysers are not readily realised with optical fibres providing the optical pathways, since the polarisations are susceptible to drift due to effects such as thermal expansion, etc., which ultimately result in diminished quality of remote entanglement.

[0009] It is an object of the disclosure to at least partly address one or more of the shortcomings in the prior art mentioned above.

[0010] According to an aspect of the disclosure, there is provided: a quantum entanglement apparatus comprising: a first interference arrangement configured to receive photons with a first polarisation from a plurality of nodes; and a second interference arrangement configured to receive photons with a second polarisation from the plurality of nodes, wherein each of the first and second interference arrangements comprises: a plurality of inputs, each input configured to receive photons from a respective node of the plurality of nodes; a plurality of outputs; and a network of paths from each input to each output, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs, wherein the first and second interference arrangements are configured such that detection of photons at the outputs of the first and second interference arrangements enables entanglement between at least two nodes of the plurality of nodes.

[0011] Advantageously, photons are separated prior to entering interference arrangements based on their polarisation mode, thereby facilitating entanglement in a stable, compact and scalable manner.

[0012] Optionally, the quantum entanglement apparatus comprises: a plurality of polarising beam splitters, wherein each polarising beam splitter is arranged to: receive photons from a respective node of the plurality of nodes; and direct received photons to the first interference arrangement or the second interference arrangement based on the polarisation of the received photons. Beneficially, conventional polarising beam splitters may be coupled with the quantum entanglement apparatus such that photons are selectively directed in accordance with their polarisation prior to entering the interference arrangements of the quantum entanglement apparatus. This facilitates more compact and hence scalable arrangements of quantum entanglement apparatuses.

[0013] Optionally, the first and second interference arrangements enable entanglement of any number of nodes up to 2nnodes, wherein n is any positive integer. Advantageously, the quantum entanglement apparatus is scalable to entangle any number of nodes in a compact fashion, thereby enabling the growth of quantum computing networks.

[0014] Optionally, the first and second interference arrangement form at least part of a photonic integrated circuit. Beneficially, the quantum entanglement apparatus may be provided in a stable and compact photonic integrated circuit that separates interference of photons in separate interferometer arrangements based on their polarisation.

[0015] Optionally, the quantum entanglement apparatus comprises two or more nodes configured to generate an entangled atom-photon pair. Optionally, the two or more nodes are each configured to generate spatially distinct photons. Advantageously, multiple entanglement paths may be provided between multiple nodes, thereby providing increasing communication paths and / or the rate of entanglement.

[0016] There is also provided a quantum repeater comprising the quantum entanglement apparatus. Beneficially, the quantum entanglement apparatus provides improved entanglement over increased distances. There is also provided a quantum entanglement multiplexer comprising a plurality of quantum entanglement apparatuses, wherein the plurality of quantum entanglement apparatuses is arranged to provide entanglement between two or more spatially distinct photons at each of the plurality of nodes. Advantageously, the entanglement multiplexer apparatus is scalable to provide multiple routes of entanglement between more than two nodes. Advantageously, increasing the number “M” of entanglement paths enables the rate of entanglement between two nodes to be increased by a factor of M.

[0017] There is also provided a method of entangling a plurality of nodes, the method comprising: generating photons at each of a plurality of nodes; directing photons with a first polarisation to a first interference arrangement and photons with a second polarisation to a second interference arrangement; at the first interference arrangement, receiving photons with the first polarisation at each input of a plurality of inputs from a respective node of the plurality of nodes; and directing the received photons to one of a plurality of outputs through a network of paths, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs; at the second interference arrangement, receiving photons with the second polarisation at each input of a plurality of inputs from a respective node of the plurality of nodes; and directing the received photons to one of a plurality of outputs through a network of paths that is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs; detecting photons at the outputs of the first and second interference arrangements; analysing detected photons to determine data; and sending the determined data to the plurality of nodes, thereby to entangle at least two nodes of the plurality of nodes.

[0018] Further aspects of the disclosure will be apparent from the description and the appended claims.

[0019] A detailed description of embodiments is described, by way of example only, with reference to the figures in which: Figure 1 shows a schematic representation of standard polarisation Bell state analyser of the prior art;

[0020] Figure 2 shows a schematic representation of a quantum entanglement apparatus with two nodes;

[0021] Figure 3 shows a flow chart of a method for entangling a plurality of nodes;

[0022] Figure 4 shows a schematic representation of an interference arrangement for entangling 2nnodes, where n=l;

[0023] Figure 5 shows a schematic representation of an interference arrangement for entangling 2nnodes, where n=2;

[0024] Figure 6 shows a schematic representation of an interference arrangement for entangling 2nnodes, where n=3;

[0025] Figure 7 shows a schematic representation of an interference arrangement for entangling 2nnodes, where n=4.

[0026] Figure 8 shows a schematic representation of a quantum entanglement apparatus with three nodes;

[0027] Figure 9 shows a schematic representation of a quantum entanglement apparatus with four nodes;

[0028] Figure 10 shows a schematic representation of the Bell state analyser of Figure 1 configured to switch entanglement between four nodes;

[0029] Figure 11 shows a schematic representation of an integrated quantum entanglement apparatus configured to switch entanglement between four nodes;

[0030] Figure 12 shows a schematic representation of a photon router apparatus;

[0031] Figure 13 shows a schematic representation of an entanglement multiplexer apparatus; and

[0032] Figure 14 shows a schematic representation of a double repeater apparatus.

[0033] In order to address at least some of the difficulties associated with known Bell state analysers (BSAs), such as those discussed with reference to Figure 1, a new photonic Bell state analyser (BSA) is described herein. The new photonic BSA is a quantum entanglement apparatus where different polarisation modes of photons generated at a plurality of nodes are separated prior to travel separate polarisation-based interferometer elements, as described in further detail with reference to Figures 2 to 14.

[0034] The quantum entanglement apparatus comprises: a first interference arrangement configured to receive photons with a first polarisation from a plurality of nodes; and a second interference arrangement configured to receive photons with a second polarisation from the plurality of nodes, wherein each of the first and second interference arrangements comprises: a plurality of inputs, each input configured to receive photons from a respective node of the plurality of nodes; a plurality of outputs; and a network of paths from each input to each output, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs, wherein the first and second interference arrangements are configured such that detection of photons at the outputs of the first and second interference arrangements enables entanglement between at least two nodes of the plurality of nodes. Optionally, the second polarisation is orthogonal to the first polarisation.

[0035] Figure 2 shows a schematic representation of a quantum entanglement apparatus 200 with two nodes 2, 4. In an example, the nodes 2, 4 are ion traps, each configured to generate photon-ion pairs in a similar manner to that described above with respect to Figure 1. In further examples, the nodes 2, 4 are configured to generate photon-ion pairs in the same ion trap. The synchronised excitation and subsequent decay of trapped ions at each of the nodes 2, 4 results in the emission of a single photon with orthogonal polarisation modes from each of the two nodes 2, 4. In further examples, the nodes 2, 4 are any suitable device for generating entangled photon-atom pairs, as described herein and may form part of the same or different devices, such as the same or different ion traps. In examples, the nodes 2, 4 include appropriate apparatus for processing and / or storing information, such that the nodes 2, 4 provide quantum computing functionality. In examples, the nodes 2, 4 comprise atomic clocks, quantum sensors, quantum memory nodes and / or quantum computers.

[0036] The quantum entanglement apparatus 200 of Figure 2 has an optical pathway 12 from the first node 2 to a polarising first beam splitter 22 and an optical pathway 14 from the second node 4 to a second polarising beam splitter 24. The first polarising beam splitter 22 is configured to provide an output to an optical pathway 202 associated with a first polarisation and an output to an optical pathway 204 associated with a second polarisation. Similarly, the second polarising beam splitter 24 is configured to provide an output to an optical pathway 206 associated with the first polarisation and an output to an optical pathway 208 associated with the second polarisation. The optical pathways 202, 206 of the first and second polarising beam splitters 22, 24 associated with the first polarisation provide inputs to a first interference arrangement 30A associated with the first polarisation and the optical pathways 204, 208 of the first and second polarising beam splitters 22, 24 associated with the second polarisation provide inputs to a second interference arrangement 30B associated with the second polarisation.

[0037] In contrast to the prior art described with respect to Figure 1, photons having both horizontal and vertical polarisation modes from each of the nodes 2, 4 are directed to respective polarising beam splitters 22, 24, rather than to a non-polarising beam splitter. The photons are directed from the nodes 2, 4 to the respective polarising beam splitters 22, 24 using any appropriate components. In an example, one or more mirrors positioned between the nodes 2, 4 and the respective polarising beam splitter 22, 24 enable photons collected from the nodes 2, 4 to be coupled to single-mode fibres providing optical pathways to the polarising beam splitters 22, 24. In further examples, optical cavities are used to collect photons generated by the nodes 2, 4 for use in the entanglement apparatus 200. In further examples a photonic integrated circuit is arranged to collect photons generated by the nodes 2, 4.

[0038] As shown at Figure 2, photons with horizontal and vertical polarisation modes are directed along an optical pathway 12 from the first node 2 to a first polarising beam splitter 22 and photons with horizontal and vertical polarisation modes are directed along an optical pathway 14 from the second node 4 to a second polarising beam splitter 24. Each of the first and second polarising beam splitters 22, 24 are configured to selectively direct photons in different directions based on the polarisation mode of the photons. In the example of Figure 2, photons with a vertical polarisation mode incident at the first polarising beam splitter 22 from the first node 2 are directed from the first polarising beam splitter 22 in a direction along an optical pathway 202 to a first interference arrangement 30A. Photons with a horizontal polarisation mode incident on the first polarising beam splitter 22 are directed from the first polarising beam splitter 22 in a direction along an optical pathway 204 to a second interference arrangement 3 OB.

[0039] Similarly, photons with a vertical polarisation mode incident at the second polarising beam splitter 24 from the second node 4 are directed from the second polarising beam splitter 24 in a direction along an optical pathway 206 to the first interference arrangement 30A. Photons with a horizontal polarisation mode incident on the second polarising beam splitter 24 are directed from the second polarising beam splitter 24 in a direction along an optical pathway 208 to a second interference arrangement 3 OB.

[0040] Accordingly, the quantum entanglement apparatus 200, comprises a plurality of polarising beam splitters 22, 24, wherein each polarising beam splitter 22, 24 is arranged to receive photons from a respective node of the plurality of nodes 2, 4 and direct received photons to the first interference arrangement 30A or the second interference arrangement 30B based on the polarisation of the received photons.

[0041] Whilst the first and second polarising beam splitters 22, 24 are shown to direct photons with a vertical polarisation to the first interference arrangement 30A and photons with a horizontal polarisation to the second interference arrangement 30B, in further examples additional, or alternative, transformations of polarisations of photons are implemented. For example, after separating polarisations of photons into horizontal and vertical polarisation modes at the first and second polarising beam splitters 22, 24, horizontal and / or vertical polarisation modes of photons can be transformed such the polarisation modes of the photons entering each of the first and second interference arrangements 30A, 30B are the same. For example, the vertical polarisation modes of photons can be transformed to horizontal polarisation modes of photons. In order to transform the polarisation mode of photons in then entanglement apparatus 200, polarisation rotators (e.g., half-wave plates) may be used to transform photons exiting the polarising beam splitters 22, 24. For example, photons having a horizontal polarisation mode exiting each of the polarising beam splitters 22, 24 may be directed through a respective polarisation rotator before being input into the second interference arrangement 3 OB such that the second interference arrangement 3 OB receives photons having a vertical polarisation mode. In such an example, both the first and second interference arrangements 30 A, 3 OB are arranged to receive photons having the same vertical polarisation mode.

[0042] Beneficially, where each independent interference arrangement 30A, 30B is configured to interfere photons with the same polarisations, the same physical construction of the interference arrangements 30A, 30B can be implemented. This is particularly advantageous in photonic integrated circuits, where the same type of waveguides can be replicated for each interference arrangement 30 A, 3 OB, thereby providing efficiency in fabrication.

[0043] The first interference arrangement 30A has two inputs provided by the optical pathways 202, 206 from the first and second polarising beam splitters 22, 24 each input configured to receive photons with a first polarisation from a respective node 2, 4. Similarly, the second interference arrangement 3 OB has two inputs provided by the optical pathways 204, 208 from the first and second polarising beam splitters 22, 24, each input configured to receive photons with a second polarisation from a respective node 2, 4.

[0044] The first interference arrangement 30A has two outputs. As shown at Figure 2, the first interference arrangement 30A has one optical output pathway 210 from the first interference arrangement 30A directed to a first photon detector 42 A associated with the first interference arrangement 30A and another optical output pathway 212 from the first interference arrangement 30A directed to a second photon detector 42B associated with the first interference arrangement 30 A.

[0045] Similarly, the second interference arrangement 30B has one optical output pathway 214 directed from the second interference arrangement 30B to a first photon detector 44 A associated with the second interference arrangement and another output pathway 216 directed from the second interference arrangement 30B to a second photon detector 44B associated with the second interference arrangement 30B.

[0046] The first interference arrangement 30A comprises a beam splitter 34A. The second interference arrangement 30B comprises a beam splitter 34B. The beam splitters 34A, 34B implement the Hong-Ou-Mandel effect, such that photons incident on the beam splitters 34A, 34B are directed to one of two outputs with a predetermined probability. In the example of Figure 2, the beam splitter 34A of the first interference arrangement 30A is configured to direct received photons along the optical pathway 210 to the first photon detector 42A with a probability of 50% and to direct received photons along the optical pathway 212 to the second photon detector 42B with a probability of 50%. Similarly, the beam splitter 34B of the second interference arrangement 30B is configured to direct received photons along the optical pathway 214 to the third photon detector 44 A with a probability of 50% and to direct received photons along the optical pathway 216 to the fourth photon detector 44B with a probability of 50%. Therefore, the first and second interference arrangements 30A, 30B each comprises at least one beam splitter 34A, 34B configured to direct received photons to one of two outputs with a predetermined probability, wherein the predetermined probability is 50% for each of the two outputs.

[0047] Accordingly, each of the first interference arrangement 30A and the second interference arrangement 30B is provided with a plurality of inputs and a plurality of outputs, and a network of paths from each input to each output, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs.

[0048] The first and second interference arrangements 30 A, 30B are configured such that detection of photons at the outputs of the first and second interference arrangements 30 A, 30B enables entanglement between at least two nodes of the plurality of nodes 2, 4, as described in further detail below, with reference to the method SI 000 set out at Figure 3.

[0049] At Figure 2 there is shown a plurality of single photon detectors 42A, 42B, 44A, 44B, each single photon detector 42A, 42B, 44A, 44B associated with a different respective output of the plurality of outputs of the first interference arrangement 30A and the plurality of outputs of the second interference arrangement 30B. The single photon detectors 42A, 42B, 44A, 44B are configured to detect photons based on the wavelength of light emitted by the nodes 2, 4. Whilst the plurality of photon detectors 42A, 42B, 44A, 44B are implemented in any appropriate manner, in an example, advantageously, the plurality of single photon detectors 42A, 42B, 44A, 44B is an integrated array 40 of single photon detectors. Advantageously, the use of an integrated array 40 of single photon detectors facilitates scaling of the quantum entanglement apparatus. This is particularly advantageous when used in combination with interference arrangements 30 A, 3 OB implemented as part of a photonic integrated circuit, allowing for a greater density of entanglement operations to be implemented. In further examples, the plurality of single photon detectors 42A, 42B, 44A, 44B for part of the same photonic integrated circuit as the first and second interference arrangements 30 A, 3 OB.

[0050] The plurality of photon detectors 42A, 42B, 44A, 44B, which optionally form part of an integrated array 40, are shown in communication with a computing device 1. The computing device 1 is in communication with the nodes 2, 4 directly, or indirectly via a network 5 of one or more further computing devices. The computing device 1 is in communication with a controller 3. Communication between the different entities forming a quantum entanglement apparatus 200 is illustrated with dashed lines and can be implemented with any appropriate combination of wired and wireless connections. In an example, the quantum entanglement apparatus 200, comprises a controller 3. In an example, the computing device 1 and / or one or more computing devices of the network 5 is a data processing device configured to analyse photons detected at the plurality of photon detectors 42 A, 42B, 44 A, 44B and communicate with the nodes 2, 4. In such cases, the quantum entanglement apparatus 200 comprises a data processing device configured to: analyse detected photons to determine data; and send the determined data to the plurality of nodes.

[0051] Beneficially, in an example, the first and second interference arrangement 30 A, 30B form at least part of a photonic integrated circuit in which one or more beam splitter and / or optical pathway is fabricated as part of the photonic integrated circuit. A photonic integrated circuit provides significant benefits in the scalability of quantum entanglement apparatus. In an example, the quantum entanglement apparatus comprises a photonic integrated circuit comprising SiN and / or AI2O3. Beneficially, such materials are suitable for processing to provide waveguiding of light with a wavelength of between 400 and 500 nm. In further examples, photonic integrated circuits comprise material to enable control of photons at different wavelengths. In an example, where trapped ions and photons operate with wavelengths of 650 nm, 1092 nm, 854 nm and / or 1550 nm, an appropriate material is used in order to fabricate photonic integrated circuits to enable the functionality of the interference arrangements 30 A, 3 OB to be implemented. In further examples, where neutral atoms (for example Rb atoms) are used to generate photons with associated wavelengths of 780 nm or 795 nm, the material of the photonic integrated circuit is determined accordingly.

[0052] Advantageously, photonic integrated circuits can be formed with high precision, thereby providing optical pathways with accurate, reproducible dimensions and providing high path length stability. This means that phase differences between interfering photons generated by different nodes can be accounted for, thereby enabling high entanglement rates and reproducibility.

[0053] In further examples, alternatively or additionally, the first and / or second interference arrangement 30A, 30B comprises one or more optical fibres configured to direct photons receivable at the respective first and / or second interference arrangement to one of the plurality of outputs.

[0054] Advantageously, the apparatus described herein uses polarising beam splitters to direct different polarisation modes of photons to different interference arrangements, thereby to enable entanglement. A method of entangling a plurality of nodes is described with reference to Figure 3. The method described with reference to Figure 3 may be implemented in different quantum entanglement apparatuses in order to entangle a plurality of any number of nodes. An example of the method of Figure 3 is described with reference to the quantum entanglement apparatus 200 of Figure 2.

[0055] Figure 3 shows a flow chart of a method SI 000 for entangling a plurality of nodes, the method comprising: generating photons at each of a plurality of nodes; directing photons with a first polarisation to a first interference arrangement and photons with a second polarisation to a second interference arrangement; at the first interference arrangement, receiving photons with the first polarisation at each input of a plurality of inputs from a respective node of the plurality of nodes; and directing the received photons to one of a plurality of outputs through a network of paths, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs; at the second interference arrangement, receiving photons with the second polarisation at each input of a plurality of inputs from a respective node of the plurality of nodes; and directing the received photons to one of a plurality of outputs through a network of paths that is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs; detecting photons at the outputs of the first and second interference arrangements; analysing detected photons to determine data; and sending the determined data to the plurality of nodes, thereby to entangle at least two nodes of the plurality of nodes.

[0056] Advantageously, the method SI 000 enables entanglement of a plurality of nodes, which include any appropriate device for generating photon pairs and processing and / or storing information as part of a quantum computing device, through the analysis of Bell states. Beneficially, the method may be implemented at least in part through the use of a photonic integrated circuit in the form of a chip providing separate interference arrangements such that photons generated by nodes and selectively separated based on the mode of polarisation are interfered separately.

[0057] The method SI 000 is initiated at step SI 002 in response to any appropriate command. In an example, the method SI 000 is at least partly implemented with a computing apparatus, such as the computing device 1 described with reference to Figure 2 and the method SI 000 is initiated in response to a computer-implemented command.

[0058] The process moves to step SI 004 where photons are generated at each of a plurality of nodes 2, 4 described with reference to Figure 2. For example, photon pairs are generated at each of the two nodes 2,4 of the quantum entanglement apparatus 200 of Figure 2 in order to entangle the two nodes 2, 4. Photons are generated at each of the nodes 2, 4 in a balanced superposition of two orthogonal polarisations. In an example, the nodes 2, 4 comprise are Paul ion traps which are subject to synchronised laser pulses in order to excite ions in each of the two nodes 2, 4. For each laser pulse and associated transition, the subsequent decay from the excited states results in the emission of a single photon with orthogonal polarisation modes from each of the two nodes 2, 4. In such cases, entangled ion-photon pairs are generated at each of the nodes 2, 4. In further examples, any suitable alternative or additional method for generating entangled photon-atom pairs at each node is implemented.

[0059] The process moves to step SI 006, where the photons generated by the plurality of nodes are selectively directed based on their polarisation, such that photons with a first polarisation are directed to a first interference arrangement 30A and photons with a second polarisation are directed to a second interference arrangement 3 OB. For example, the first polarising beam splitter 22 of the quantum entanglement apparatus 200 of Figure 2 receives photons directed along the optical pathway 12 from the first node 2 and directs a first polarisation mode of the photons along the optical pathway 202 to the first interference arrangement 30A and directs a second polarisation mode of the photons, orthogonal to the first polarisation mode along the optical pathway 204 to the second interference arrangement 30B. Similarly, the second polarising beam splitter 24 of the quantum entanglement apparatus 200 of Figure 2 receives photons directed along the optical pathway 14 from the second node 4 and directs a first polarisation mode of the photons along the optical pathway 206 to the first interference arrangement 30A and directs a second polarisation mode of the photons, orthogonal to the first polarisation mode, along the optical pathway 208 to the second interference arrangement 30B. Whilst the first and second polarising beam splitters 22, 24 are described as directing photons with a first polarisation mode to the first interference arrangement 30A and photons with a second polarisation mode to the second interference arrangement 30B where the second polarisation mode is orthogonal to the first polarisation mode, in further examples additional, or alternative, transformations of polarisations of photons are implemented.

[0060] For example, after separating polarisations into horizontal and vertical polarisation modes at the first and second polarising beam splitters 22, 24 horizontal and / or vertical polarisation modes of photons can be transformed such the polarisation modes of the photons entering each of the first and second interference arrangements 30 A, 30B are the same. For example, the vertical polarisation modes of photons can be transformed to horizontal polarisation modes of photons. In order to transform the polarisation mode of photons in then entanglement apparatus 200, polarisation rotators (e.g., half-wave plates) may be used to transform photons exiting the polarising beam splitters 22, 24. For example, photons having a horizontal polarisation mode exiting each of the polarising beam splitters 22, 24 may be directed through a respective polarisation rotator before being input into the second interference arrangement 3 OB such that the second interference arrangement 30B receives photons having a vertical polarisation mode. In such an example, both the first and second interference arrangements 30 A, 3 OB are arranged to receive photons having the same vertical polarisation mode.

[0061] Once the photons have been selectively directed based on their polarisation and, optionally, the polarisation of the photons has been transformed for further processing, the process then moves to step SI 008, where the photons generated by the plurality of nodes and selectively directed to the first or second interference arrangement 30A, 30B based on their polarisation pass through the interference arrangements 30A, 3 OB. Accordingly, the first interference arrangement 30A receives photons with the first polarisation at each input of a plurality of inputs from a respective node of the plurality of nodes and directs the received photons to one of a plurality of outputs through a network of paths, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs. Similarly the second interference arrangement 30B receives photons with the second polarisation at each input of a plurality of inputs from a respective node of the plurality of nodes and directs the received photons to one of a plurality of outputs through a network of paths that is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs.

[0062] The process then moves to step S1010 where photons are detected at the outputs of the first and second interference arrangements 30 A, 3 OB. Photons are detected at the photon detectors 42 A, 42B associated with the first interference arrangement 30A and photon detectors 44 A, 44B associated with the second interference arrangement 3 OB. Detected photons at the photon detectors 42A, 42B, 44A, 44B provide signals via any suitable communication pathway to the computing device 1. The process then moves to step S 1012, wherein the detected photons are analysed to determine data. In an example, the detected photons are analysed at the computing device 1 which is a data processing device configured to analyse photons detected at the plurality of photon detectors 42 A, 42B, 44 A, 44B. Coincidental determination of the detection of two photons , which may be two photons with orthogonal polarisation, in two different single photon detectors heralds entanglement. Accordingly, analysis of Bell states enables quantum entanglement between a plurality of quantum computing nodes. Any additional or alternative method for processing data in order to determine entanglement is implemented in further examples.

[0063] The process then moves to step S 1014, where determined data is sent to the plurality of nodes, thereby to entangle at least two nodes of the plurality of nodes. For example, where entanglement has been heralded, the information is communicated to the nodes 2, 4 through any appropriate communication pathway. Entanglement between ionphoton pairs at each of the nodes 2, 4 is transferred to provide entanglement between the ions of the nodes 2, 4, thereby entangling the nodes 2, 4. The entanglement between the nodes 2, 4 can then be exploited in any suitable manner.

[0064] The process ends at step S1016. Alternatively, or additionally, further steps are implemented. In further examples, the order of the steps of the method SI 000 is provided in any appropriate order in order to implement the functionality described herein. For example, steps may be performed sequentially and / or in parallel as appropriate. Further, all or part of the process SI 000 may be repeated in order to generate and / or exploit entanglement of a plurality of nodes. For example, the process S1000 is typically repeated in order to provide a high rate of generation of single photons (of the order of millions per second) at the nodes 2, 4, thereby increasing the rate of successful entanglement between the nodes 2, 4.

[0065] Whilst the process of entangling a plurality of nodes is described with reference to a two-node system of Figure 2, in further examples, the method SI 000 of entangling a plurality of nodes is applicable to quantum entanglement apparatuses configured to entangle any number of nodes, such as the node described with reference to Figure 2. For example, the method SI 000 is applicable to quantum entanglement apparatuses comprising the interference arrangements 30 A, 3 OB described with reference to Figures 4 to 7, in order to entangle 2nnodes. In further examples, the method SI 000 is applicable to the 3 node quantum entanglement apparatus 800 described with reference to Figure 8 and the 4 node quantum entanglement apparatus 900 described with reference to Figure 9. In further examples, combinations of the interference arrangements described herein are implemented additionally or alternatively in order to provide the necessary interference of photons to herald entanglement.

[0066] Whilst the method SI 000 described with reference to Figure 3 is described with reference to the generation of a photon pair at each of a first node and a second node, alternatively or additionally, the method SI 000 comprises generating one or more entangled atom-photon pair at each of two or more nodes. In an example, generating one or more entangled atom-photon pair at one of the two or more modes comprises: trapping an ion or neutral atom; and exciting an electronic transition of the trapped ion or neutral atom, such that the subsequent decay generates an entangled atom-photon pair at the node. In further examples, generating one or more entangled atom-photon pair at each of two of more nodes comprises any appropriate alternative or additional process for generating an entangled atom-photon pair at the node.

[0067] Whilst the first and second interference arrangements 30 A, 30B of Figure 2 are arranged for the entanglement of two nodes 2, 4, in further examples the first and second interference arrangements 30 A, 30B are configured for the entanglement of more than two nodes. For example, optionally the quantum entanglement apparatus described herein comprises a first and second interference arrangement 30A, 30B, wherein the first and second interference arrangements 30A, 30B enable entanglement of at least three nodes or at least four nodes. For example, three node entanglement is described with reference to Figure 8 and four node entanglement is described with reference to Figure 9. Whilst the quantum entanglement apparatuses shown at Figures 8 and 9 do not illustrate the computing device 1, controller 3 and network of one or more computing devices 5, it is understood that in further examples, these and / or additional apparatus are implemented in order to establish entanglement between nodes and subsequent functional applications. Beneficially, the quantum entanglement apparatus described herein may be scaled in order to entangle photons from any number of nodes. Examples of interference arrangements 30 A, 3 OB that can be used to adapt the quantum entanglement apparatus 200 of Figure 2 to entangle additional nodes are shown at Figures 4 to 7. In such cases, the number of nodes of the quantum entanglement apparatus is adapted to the number of inputs of the interference arrangements 30 A, 3 OB of the quantum entanglement apparatus and the number of photon detectors is adapted to the number of outputs of the interference arrangements 30 A, 30B of the quantum entanglement apparatus. In further examples, the quantum entanglement apparatus described herein may be scaled such that photons from any number of nodes are entangled through selective use of inputs. For example, the same quantum entanglement apparatus may be used to receive photons selectively at a subset of the inputs in order to entangle a number of nodes corresponding to the selected subset of the inputs by detecting photons at the outputs of the quantum entanglement apparatus. For example, Figure 6 describes the use of an 8-node interferometer using interference arrangements 30A, 30B that may be used to entangle 2, 3, 4, 5, 6, 7 and 8 nodes, through the selective use of inputs of the interference arrangements 30 A, 30B.

[0068] The examples of Figures 4 to 7 show optical pathways represented schematically with lines extending from each input of the interference arrangement 30 A, 30B to each output of the interference arrangement 30 A, 30B. The optical pathways are shown to cross one another in order to illustrate how the interference arrangements are scaled to entangle nodes. However, intersection of the optical pathways occurs at beam splitters and optical pathways may otherwise be implemented with different physical realisations. The beam splitters implement the Hong-Ou-Mandel effect as described herein, such that photons entering a beam splitter are directed to one of two outputs with a predetermined probability. In the examples of Figures 4 to 7, the predetermined probability for each output of a beam splitter is 50%. However, in further examples, different schemes and probability distributions are implemented in order to entangle multiple nodes. In an example, the interference arrangements 30A, 30B of Figure 4 to 7 are implemented as photonic integrated circuits that are fabricated with any appropriate arrangement, size and shape of two-dimensional and / or three-dimensional configuration to provide the functionality described herein.

[0069] Whilst Figures 4 to 7 each show one interference arrangement 30A, 30B, it is understood that the interference arrangements 30 A, 3 OB are shown individually for ease of reference. However, it is understood that in the context of a quantum entanglement apparatus where different polarisation modes of photons are separated prior to entry in the interference arrangements 30A, 30B, a quantum entanglement apparatus is provided with two separate interference arrangements 30 A, 3 OB. Accordingly, one interference arrangement 30A is configured to receive photons with a first polarisation from a plurality of nodes and the other interference arrangement 3 OB is configured to receive photons with a second polarisation from the plurality of nodes. Optionally, the second polarisation is orthogonal to the first polarisation. Effectively, a quantum entanglement apparatus is formed through the duplication of interference arrangements, such as those described with reference to Figures 4 to 7 to provide two interference arrangements 30 A, 3 OB in a quantum entanglement apparatus. Accordingly, such duplicated interference arrangements 30 A, 3 OB (which optionally do not form part of a photonic integrated circuit, or optionally form part of the same or different photonic integrated circuit) are arranged in an analogous fashion to that described with reference to the quantum entanglement apparatus 200 of Figure 2, providing a first interference arrangement 30A configured to receive photons with a first polarisation from a plurality of nodes and a second interference arrangement 30B configured to receive photons with a second polarisation from the plurality of nodes.

[0070] The quantum entanglement apparatus 200 described with reference to Figure 2 may be adapted such that the first and second interference arrangements 30 A, 30B enable entanglement of any number of nodes up to 2nnodes, wherein n is any positive integer. In the examples shown at Figures 4 to 7, a scheme for scaling entanglement to 2nnodes, wherein n is any positive integer is illustrated, thereby enabling entanglement of any number of nodes up to 2nnodes. In the examples of Figures 4 to 7, each of the first and second interference arrangements 30A, 30 B comprise: 2ninputs, each input configured to receive photons from a respective node of the plurality of nodes; 2noutputs; and n subnetworks of the network of paths, wherein each sub-network comprises 2n / 2 beam splitters. Further, in the examples of Figures 4 to 7, each interference arrangement comprises a first sub-network, wherein each beam splitter of the first sub-network is configured to: receive polarised light from a different pair of inputs of the 2ninputs; and provide a pair of outputs. In the examples of Figures 4 to 7, the n sub-networks are arranged in an sequence of i=l to n sub-networks, wherein the outputs of each ithsub-network provides inputs for the (i+l)thsub-network, from i=l to (n-1). In the examples of Figures 4 to 7, the 2n / 2 beam splitters of each ithsub-network are arranged in 2(n-1)groups, wherein each group is configured to mix inputs from a different two groups of the (i-l)thsub-network and provide outputs.

[0071] Whilst examples of a scheme for scaling the interference arrangements 30A, 30B to entangle 2nnodes are shown, any appropriate alternative and / or additional schemes for scaling the interference arrangements to entangle 2nnodes are implemented in further examples.

[0072] Figure 4 shows a schematic representation of an interference arrangement 30 A, 3 OB for entangling 2nnodes, where n=l. The interference arrangement 30 A, 3 OB may be implemented in a quantum entanglement apparatus such that each of the first and second interference arrangements 30A, 30B comprise: 21=2 inputs, each input configured to receive photons from a respective node of the plurality of nodes; 21=2 outputs, where each output is provided to a photon detector; and 1 sub-networks of the network of paths, wherein each sub-network comprises 2V2 = 1 beam splitter.

[0073] In the example of Figure 4 the interference arrangement 30A, 30B is the first subnetwork 402, wherein the beam splitter 404 of the first sub-network 402 is configured to: receive polarised light from a different pair of inputs 401 A, 40 IB of the 2 inputs, which in the case of 21inputs, is the pair of inputs; and provide a pair of outputs. Accordingly, in the example of Figure 4, the sub-network 402 is arranged in a sequence of 1 sub-network 402, wherein the outputs 403 A, 403B of the sub-network 402 provide inputs for photon detectors (shown as an integrated photon detector array 40 at Figure 4). In the example of Figure 4, the beam splitter 404 of the sub-network 402 is arranged in 1 group, wherein the group is configured to mix the two inputs from the nodes and provide two outputs. Advantageously, the interference arrangement 30 A, 3 OB described with reference to Figure 4 can effectively be used as a building block of a first sub-network 402 of interference arrangements 30A, 30B associated with a polarisation mode in order to scale the entanglement apparatus to 2nnodes, where n is a positive integer, by replicating the arrangement of inputs 401 A, 401B, beam splitter 404 and outputs 403 A, 403B to couple to further pairs of nodes and to provide further outputs serving as inputs to a subsequent subnetwork of the interference arrangement 30 A, 30B.

[0074] Figure 5 shows a schematic representation of an interference arrangement 30 A, 30B for entangling 2nnodes, where n=2. There is shown an interference arrangement 30A, 30B which has a first sub-network 402 and a second sub-network 502.

[0075] The interference arrangement 30A, 30B of Figure 2 may be replicated to provide two interference arrangements 30 A, 30B wherein one of the interference arrangements 30A is configured to receive photons with a first polarisation from a plurality of nodes and wherein the other interference arrangement 30B is configured to receive photons with a second polarisation from the plurality of nodes, as described herein. Optionally, the second polarisation is orthogonal to the first polarisation.

[0076] In the example of Figure 5, the first and second interference arrangements 30A, 30B enable entanglement of 22=4 nodes. In such cases, the quantum entanglement apparatus is provided such that each of the first and second interference arrangements 30A, 30B comprise: 22=4 inputs 401A, 401B, 401C, 401D, each input configured to receive photons from a respective node of the plurality of nodes; 22=4 outputs 503 A, 503B, 503C, 503D; and 2 sub-networks 402, 502 of the network of paths, wherein each sub-network 402, 502 comprises 22 / 2=2 beam splitters.

[0077] In application of the example of Figure 5, the quantum entanglement apparatus comprises a first sub-network 402, wherein each beam splitter 404 of the first sub-network 402 is configured to: receive polarised light from a different pair of inputs of the 22=4 inputs 401 A, 401B, 401C, 401D; and provide a pair of outputs. In contrast to the interference arrangement 30A, 30B of Figure 4, outputs 403 A, 403B of the first subnetwork 402 connect to inputs of the second sub-network 502 at an interface 412 between the first sub-network 402 and the second sub-network 502, thereby to provide inputs at the second sub-network 502. It is understood that whilst the interface 412 emphasises the repeating patterns of the first sub-network 402 and the second sub-network 502, in further examples the optical pathways are provide in any appropriate implementation such that photons are enabled to travel seamlessly from the inputs of the interference arrangements 30 A, 3 OB to the outputs of the interference arrangements 30 A, 30B.

[0078] In the example of Figure 5, the 2 sub-networks 402, 502 are arranged in a sequence of i=l to 2 sub-networks 402, 502, wherein the outputs of each ithsub-network provides inputs for the (i+l)thsub-network, from i=l to (n-1). The second sub-network 502 provides outputs 503 A, 503B, 503C, 503D to photon detectors 40 (shown as an integrated photon detector array 40 at Figure 5). In the example of Figure 5, the 22 / 2 = 2 beam splitters of each ithsub-network are arranged in 2(n-1)groups (i.e., 2(2-1)= 2 in the i=l subnetwork 402 and 2(2'2)= 1 in the i=2 sub-network 502), wherein each group is configured to mix inputs from a different two groups of the (i-l)thsub-network and provide outputs. For example, the i=l sub-network has beam splitters 404 arranged in 2 groups and the i=2 sub-network 1202 has beam splitters 504 arranged in 1 group.

[0079] As shown at Figure 5, for the i=l sub-network 402, each beam splitter 404 receives photons from a different pair of inputs of the 4 inputs, each input receiving photons from a respective node. The beam splitters 404 of the first sub-network 402 are arranged in two groups. For the i=2 sub-network 502, there is one group of beam splitters 504 that is configured to mix inputs from a different two groups of the first sub-network 402. Therefore, the interference arrangement 30 A, 30B of Figure 5 shows how photons from four nodes are coupled into the interference arrangement 30 A, 30B such that a network of paths from each input to each output is provided, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs.

[0080] Advantageously, the interference arrangement 30 A, 30B described with reference to Figure 5 can be used as a building block of a first and second sub-networks 402, 502 of interference arrangements 30A, 30B associated with a polarisation mode in order to scale the entanglement apparatus to 2nnodes, where n is a positive integer. Effectively, the interference arrangement 30A, 30B described with reference to Figure 5 is duplicated such that two interference arrangements feed into a further sub-network.

[0081] Figure 6 shows a schematic representation of an interference arrangement 30 A, 3 OB for entangling 2nnodes, where n=3. There is shown an interference arrangement 30 A, 30B which has a first sub-network 402, a second sub-network 502 and a third sub-network 602. The first sub-network 402 and the second sub-network 502 of the interference arrangement 30 A, 30B comprises a pair of the interference arrangements 30 A, 30B for entangling four nodes, as described with reference to Figure 5. The interference arrangement 30A, 30B of Figure 6 may be replicated to provide two interference arrangements 30 A, 30B wherein one of the interference arrangements 30A is configured to receive photons with a first polarisation from a plurality of nodes and wherein the other interference arrangement 30B is configured to receive photons with a second polarisation from the plurality of nodes, as described herein. Optionally, the second polarisation is orthogonal to the first polarisation.

[0082] In the example of Figure 6, the first and second interference arrangements 30 A, 30B enable entanglement of 23=8 nodes. In such cases, the quantum entanglement apparatus is provided such that each of the first and second interference arrangements 30 A, 30B comprise: 23=8 inputs 401 A to 401H, each input 401 A to 401H configured to receive photons from a respective node of the plurality of nodes; 23=8 outputs 603 A to 603H; and 3 sub-networks 402, 502, 602 of the network of paths, wherein each sub-network 402, 502, 602 comprises 23 / 2 = 4 beam splitters. In application of the example of Figure 6, quantum entanglement apparatus comprises a first sub-network 402, wherein each beam splitter 404 of the first sub-network 402 is configured to: receive polarised light from a different pair of inputs of the 23= 8 inputs; and provide a pair of outputs. In the example of Figure 6, the 3 sub-networks 402, 502, 602 are arranged in an sequence of i=l to 3 sub-networks 402, 502, 602, wherein the outputs of each ithsub-network provides inputs for the (i+l)thsub-network, from i=l to (n-1). In the example of Figure 6, the 23 / 2=4 beam splitters of each ithsub-network are arranged in 2(3-1)groups, wherein each group is configured to mix inputs from a different two groups of the (i-l)thsub-network and provide outputs. For example, the i=l sub-network 402 comprises 4 beam splitters 404 in 4 groups. The i=2 sub-network 502 comprises 4 beam splitters 504 in 2 groups and the i=3 sub-network 602 comprises 4 beam splitters 604 in 1 group.

[0083] In an analogous manner to that described with reference to Figure 5, outputs 403 A, 403B of the first sub-network 402 connect to inputs of the second sub-network 502 at an interface 412 between the first sub-network 402 and the second sub-network 502, thereby to provide inputs at the second sub-network 502. Similarly, outputs from the second subnetwork 502 connect to inputs of the third sub-network 602 at an interface 512 between the second sub-network 502 and the third sub-network 602. It is understood that whilst the interfaces 412, 512 emphasise the repeating patterns of the first sub-network 402, second sub-network 502 and the third sub-network 502, in further examples the optical pathways are provide in any appropriate implementation such that photons are enabled to travel seamlessly from the inputs of the interference arrangements 30 A, 30B to the outputs of the interference arrangements 30 A, 30B.

[0084] As shown at Figure 6, for the i=l sub-network 402, each beam splitter 404 receives photons from a different pair of inputs of the 8 inputs, each input receiving photons from a respective node. The beam splitters 404 of the first sub-network 402 are arranged in four groups. For the i=2 sub-network 502, there are two groups of two beam splitters 504 that are each configured to mix inputs from a different two groups of one beam splitter the first sub-network 402. For the i=3 sub-network 602, there is one group of four beam splitters 604 that is configured to mix inputs from a different two groups of two beam splitters 504 of the second sub-network 502.

[0085] Therefore, the interference arrangement 30 A, 30B of Figure 6 shows how photons from four nodes are coupled into the interference arrangement 30 A, 30B such that a network of paths from each input to each output is provided, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs.

[0086] Advantageously, the interference arrangement 30 A, 30B described with reference to Figure 6 can be used as a building block of first, second and third sub-networks 402, 502, 602 of interference arrangements 30A, 30B associated with a polarisation mode in order to scale the entanglement apparatus to 2nnodes, where n is a positive integer. Effectively, the interference arrangement 30A, 30B described with reference to Figure 6 is duplicated such that two interference arrangements feed into a further sub-network.

[0087] Figure 7 shows a schematic representation of an interference arrangement 30 A, 30B for entangling 2nnodes, where n=4. The interference arrangement 30A, 30B builds on the structure described with reference to Figures 4 to 6, showing how the interference arrangement 30A, 30B is scalable to enable entanglement of 2nnodes. The interference arrangement 30A, 30B of Figure 7 may be replicated to provide two interference arrangements 30 A, 3 OB wherein one of the interference arrangements 30A is configured to receive photons with a first polarisation from a plurality of nodes and wherein the other interference arrangement 30B is configured to receive photons with a second polarisation from the plurality of nodes, as described herein. Optionally, the second polarisation is orthogonal to the first polarisation.

[0088] In the example of Figure 7, the first and second interference arrangements 30 A, 30B enable entanglement of 24=16 nodes. In such cases, the quantum entanglement apparatus is provided such that each of the first and second interference arrangements comprise: 24=16 inputs 401 A to 40 IP, each input 401 A to 40 IP configured to receive photons from a respective node of the plurality of nodes; 24=16 outputs; and 4 subnetworks 402, 502, 602, 702 of the network of paths, wherein each sub-network 402, 502, 602, 702 comprises 24 / 2 = 8 beam splitters.

[0089] In the example of Figure 7, the quantum entanglement apparatus comprises a first sub-network 402, wherein each beam splitter 404 of the first sub-network 402 is configured to: receive polarised light from a different pair of inputs of the 24= 16 inputs 401 A to 401P; and provide a pair of outputs. In the example of Figure 7, the 4 subnetworks 402, 502, 602, 702 are arranged in an sequence of i=l to 4 sub-networks, wherein the outputs of each ithsub-network provides inputs for the (i+l)thsub-network, from i=l to (n-1). In the example of Figure 7, the 24 / 2=8 beam splitters of each ithsubnetwork are arranged in 2(4-1)groups, wherein each group is configured to mix inputs from a different two groups of the (I-l)thsub-network and provide outputs. For example, the i=l sub-network 402 comprises 8 beam splitters 404 in 8 groups. The i=2 sub-network 502 comprises 8 beam splitters 504 in 4 groups, the i=3 sub-network 602 comprises 8 beam splitters 604 in 2 groups and the i=4 sub-network 702 comprises 8 beam splitters 704 in 1 group.

[0090] In an analogous manner to that described with reference to Figure 6, outputs 403 A, 403B of the first sub-network 402 connect to inputs of the second sub-network 502 at an interface 412 between the first sub-network 402 and the second sub-network 502, thereby to provide inputs at the second sub-network 502. Similarly, outputs from the second subnetwork 502 connect to inputs of the third sub-network 602 at an interface 512 between the second sub-network 502 and the third sub-network 602. Similarly, outputs from the third sub-network 602 connect to inputs of the fourth sub-network 702 at an interface 612 between the third sub-network 602 and the fourth sub-network 702. It is understood that whilst the interfaces 412, 512, 612 emphasise the repeating patterns of the first subnetwork 402, second sub-network 502, third sub-network 502 and the fourth sub-network 602, in further examples the optical pathways are provide in any appropriate implementation such that photons are enabled to travel seamlessly from the inputs of the interference arrangements 30 A, 30B to the outputs of the interference arrangements 30 A, 30B.

[0091] Beneficially, the new Bell state analyser arrangement described herein can be extended to entangle quantum networks composed of n-nodes using an entanglement swapping technique. Advantageously, by separating the polarisations at the input, reliable construction by replicating only networks of beams splitters is enabled. As described herein, in an example, the polarisation modes of photons may be split, for example using polarising beam splitters, to provide two different photon polarisation modes for interference at separate interference arrangements. In some examples, one or both of the two different photon polarisation modes is transformed using one or more optical components before being input into the respective interference arrangement. Beneficially, the same interference construction, for example the same beams splitter network hardware, is used for both interference arrangements in cases where one or both of the different polarisation photon modes is transformed such that both polarisation photon modes are the same for each interference arrangement. As shown at Figure 7, for the i=l sub-network 402, each beam splitter 404 receives photons from a different pair of inputs of the 16 inputs 401 A to 401P, each input receiving photons from a respective node. The beam splitters 404 of the first sub-network 402 are arranged in eight groups. For the i=2 sub-network 502, there are four groups of two beam splitters 504 that are each configured to mix inputs from a different two groups of one beam splitter 404 the first sub-network 402. For the i=3 sub-network 602, there are two groups of four beam splitters 604 that are configured to mix inputs from a different two groups of two beam splitters 504 of the second sub-network 502. For the i=4 sub-network 702 there is one group of eight beam splitters 703 that is configured to mix inputs from a different two groups of four beam splitters 604 of the third sub-network 602.

[0092] Therefore, the interference arrangement 30 A, 30B of Figure 7 shows how photons from sixteen nodes are coupled into the interference arrangement 30 A, 30B such that a network of paths from each input to each output is provided, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs. By following the pattern of increasing the number of sub-networks, entanglement can be provided for 2nnodes.

[0093] Whilst a quantum entanglement apparatus implementing the method SI 000 of Figure 3 can be provided using the interference arrangements 30 A, 30B described with respect to scaling to 2nnodes, in further examples entanglement can be provided between any number of nodes using suitably arranged interference arrangements 30 A, 30B.

[0094] For example, Figure 8 shows a schematic representation of a quantum entanglement apparatus 800 with three nodes 2, 4, 6. Figure 8 illustrates a Bell state analyser that allows for the creation of multiparticle entanglement between 3 nodes, using linear optics and non-number resolved photon detectors. There is shown a first interference arrangement 30A and a second interference arrangement 30B. The first interference arrangement 30A is configured to receive photons with a first polarisation from a plurality of nodes 2, 4, 6; and the second interference arrangement 30B is configured to receive photons with a second polarisation from the plurality of nodes 2, 4, 6, wherein each of the first and second interference arrangements 30 A, 30B comprises: a plurality of inputs, each input configured to receive photons from a respective node of the plurality of nodes 2, 4, 6; a plurality of outputs; and a network of paths from each input to each output, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs, wherein the first and second interference arrangements 30 A, 3 OB are configured such that detection of at least two photons at the outputs of the first and second interference arrangements enables entanglement between at least two nodes of the plurality of nodes 2, 4, 6. Optionally, the second polarisation is orthogonal to the first polarisation.

[0095] In the example of Figure 8, there are three nodes 2, 4, 6, each configured to generate entangled atom-photon pairs. As shown at Figure 8, photons with horizontal and vertical polarisation modes are directed along an optical pathway 12 from the first node 2 to a first polarising beam splitter 22. Photons with horizontal and vertical polarisation modes are directed along an optical pathway 14 from the second node 4 to a second polarising beam splitter 24. Photons with horizontal and vertical polarisation modes are directed along an optical pathway 16 from the third node 6 to a third polarising beam splitter 26. Each of the first, second and third polarising beam splitters 22, 24, 26 are configured to selectively direct photons in different directions based on the polarisation mode of the photons.

[0096] In an analogous manner to that described with reference to Figure 2, in the example of Figure 8, photons with a vertical polarisation mode incident at the first polarising beam splitter 22 from the first node 2 are directed from the first polarising beam splitter 22 to a first interference arrangement 30 A. Photons with a horizontal polarisation mode incident on the first polarising beam splitter 22 are directed to a second interference arrangement 30B. Similarly, photons with a vertical polarisation mode incident at the second polarising beam splitter 24 from the second node 4 are directed from the second polarising beam splitter to the first interference arrangement 30A and photons with a horizontal polarisation mode incident on the second polarising beam splitter 24 are directed to the second interference arrangement 3 OB. Similarly, photons with a vertical polarisation mode incident at the third polarising beam splitter 26 from the third node 6 are directed to the first interference arrangement 30A and photons with a horizontal polarisation mode are directed to the second interference arrangement 3 OB.

[0097] Whilst the first, second and third polarising beam splitters 22, 24, 26 are shown to direct photons with a vertical polarisation to the first interference arrangement 30A and photons with a horizontal polarisation to the second interference arrangement 30B, in further examples additional, or alternative, transformations of polarisations of photons are implemented. For example, after separating polarisations into horizontal and vertical polarisation modes at the first, second and third polarising beam splitters 22, 24, 26, horizontal and / or vertical polarisation modes of photons can be transformed such the polarisation modes of the photons entering each of the first and second interference arrangements 30A, 30B are the same. For example, the vertical polarisation modes of photons can be transformed to horizontal polarisation modes of photons. In order to transform the polarisation mode of photons in then entanglement apparatus 200, polarisation rotators (e.g., half-wave plates) may be used to transform photons exiting the polarising beam splitters 22, 24, 26. For example, photons having a horizontal polarisation mode exiting each of the polarising beam splitters 22, 24, 26 may be directed through a respective polarisation rotator before being input into the second interference arrangement 3 OB such that the second interference arrangement 3 OB receives photons having a vertical polarisation mode. In such an example, both the first and second interference arrangements 30 A, 3 OB are arranged to receive photons having the same vertical polarisation mode.

[0098] Beneficially, where each independent interference arrangement 30A, 30B is configured to interfere photons with the same polarisations, the same physical construction of the interference arrangements 30A, 30B can be implemented. This is particularly advantageous in photonic integrated circuits, where the same type of waveguides can be replicated for each interference arrangement 30 A, 3 OB, thereby providing efficiency in fabrication.

[0099] Accordingly, the quantum entanglement apparatus 800, comprises: a plurality of polarising beam splitters 22, 24, 26 wherein each polarising beam splitter 22, 24, 26 is arranged to: receive photons from a respective node of the plurality of nodes 2, 4, 6; and direct received photons to the first interference arrangement 30A or the second interference arrangement 30B based on the polarisation of the received photons.

[0100] The first interference arrangement 30A has three inputs provided by the optical pathways from each of the first, second and third polarising beam splitters 22, 24, 26 each input configured to receive photons with a first polarisation from a respective node 2, 4, 6. Similarly, the second interference arrangement 3 OB has three inputs provided by the optical pathways from each of the first, second and third polarising beam splitters 22, 24, 26, each input configured to receive photons with a second polarisation from a respective node 2, 4, 6.

[0101] The first interference arrangement 30A has three outputs. As shown at Figure 8, the first interference arrangement 30A has one output path from the first interference arrangement 30A directed to a first photon detector 42 A associated with the first interference arrangement 30 A, another output path from the first interference arrangement 30A directed to a second photon detector 42B associated with the first interference arrangement 30 A, and yet another output path from the first interference arrangement 30A directed to a third photon detector 42C associated with the first interference arrangement 30 A. Similarly, the second interference arrangement 3 OB has one output path directed from the second interference arrangement 3 OB to a first photon detector 44 A associated with the second interference arrangement 3 OB, another output path directed from the second interference arrangement 3 OB to a second photon detector 44B associated with the second interference arrangement 3 OB and yet another output path directed from the second interference arrangement 3 OB to a third photon detector 44C associated with the second interference arrangement 3 OB.

[0102] Each of the first interference arrangement 30A and the second interference arrangement 30B of the quantum entanglement apparatus 800 of Figure 8 provides a network of paths from each input to each output, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs. As shown at Figure 8, the network of paths of the first and second interference arrangements 30A, 30B each comprise: a first beam splitter 34A, 34B configured to: receive photons from a first node 2 and a second node 4 of the plurality of nodes 2, 4, 6; and direct received photons to one of two outputs of the first beam splitter 34 A, 34B with a predetermined probability; a second beam splitter 35A, 35B configured to: receive photons from a third node 6 of the plurality of nodes 2, 4, 6 and an output of the first beam splitter 34 A, 34B; and direct received photons to one of two outputs with a predetermined probability; and a third beam splitter 38 A, 38B configured to: receive photons from the other output of the first beam splitter 34A, 34B and an output of the second beam splitter 35 A, 35B; and direct received photons to one of two outputs with a predetermined probability.

[0103] As shown at Figure 8, the two outputs of the third beam splitter 38A of the first interference arrangement 30A are directed to respective first and second photon detectors 42 A, 42B associated with the first interference arrangement 30 A. The other output of the second beam splitter 35A of the first interference arrangement 30A that is not directed to the third beam splitter 35 A is directed to a third photon detector 42C associated with the first interference arrangement 30 A. The two outputs of the third beam splitter 38B of the second interference arrangement 3 OB are directed to respective first and second photon detectors 44 A, 44B associated with the second interference arrangement 3 OB. The other output of the second beam splitter 35B of the second interference arrangement 30B that is not directed to the third beam splitter 35B is directed to a third photon detector 44C associated with the first interference arrangement 3 OB. With such arrangements, all of the inputs with a first polarisation from respective nodes 2, 4, 6 of the plurality of nodes 2, 4, 6 are provided with a pathway to each of the photon detectors 42A, 42B, 42C associated with the first interference arrangement 30A and all of the inputs with a second polarisation from respective nodes 2, 4, 6 of the plurality of nodes 2, 4, 6 are provided with a pathway to each of the photon detectors 44A, 44B, 44C associated with the second interference arrangement 3 OB.

[0104] In the example of the quantum entanglement apparatus 800 of Figure 8, the first and / or second interference arrangement comprises at least one beam splitter configured to direct received photons to one of two outputs with a predetermined probability. The first beam splitter 34A, 34B of each of the first and second interference arrangements 30A, 30B has a predetermined probability that is 50% for each of the two outputs. Similarly, the third beam splitter 38 A, 38B of each of the first and second interference arrangements 30A, 30B has a predetermined probability that is 50% for each of the two outputs. In contrast, the second beam splitter 35 A, 35B of each of the first and second interference arrangements 30A, 30B has a 1 :2 predetermined probability ratio of inputs being reflected or transmitted at the second beam splitter 35 A, 35B. In the case of a three node system, this ensures that the balance of probabilities of photons detected at the photon detectors associated with each of the first and second interference arrangements 30A, 30B is sufficiently balanced in order to enable entanglement between three nodes 2, 4, 6.

[0105] Figure 9 shows a schematic representation of a quantum entanglement apparatus 900 with four nodes 2, 4, 6, 8. Advantageously, Figure 9 shows a Bell state analyser that can entangle 4 nodes in a multiparticle entangled state using only linear optics and nonnumber resolved photon detectors. The quantum entanglement apparatus 900 of Figure 9 shows an alternative representation of the interference arrangements 30 A, 30B described with reference to Figure 5 and implements the same functionality.

[0106] There is shown a first interference arrangement 30 A and a second interference arrangement 30B. The first interference arrangement 30A is configured to receive photons with a first polarisation from a plurality of nodes 2, 4, 6, 8; and the second interference arrangement 30B is configured to receive photons with a second polarisation from the plurality of nodes 2, 4, 6, 8, wherein each of the first and second interference arrangements 30 A, 30B comprises: a plurality of inputs, each input configured to receive photons from a respective node of the plurality of nodes 2, 4, 6, 8; a plurality of outputs; and a network of paths from each input to each output, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs, wherein the first and second interference arrangements 30 A, 30B are configured such that detection of photons at the outputs of the first and second interference arrangements enables entanglement between at least two nodes of the plurality of nodes 2, 4, 6, 8. In the example of Figure 9, there are four nodes 2, 4, 6, 8, each configured to generate entangled atom-photon pairs. As shown at Figure 9, photons with horizontal and vertical polarisation modes are directed along an optical pathway 12 from the first node 2 to a first polarising beam splitter 22. Photons with horizontal and vertical polarisation modes are directed along an optical pathway 14 from the second node 4 to a second polarising beam splitter 24. Photons with horizontal and vertical polarisation modes are directed along an optical pathway 16 from the third node 6 to a third polarising beam splitter 26. Photons with horizontal and vertical polarisation modes are directed along an optical pathway 18 from the fourth node 8 to a fourth polarising beam splitter 28. Each of the first, second, third and fourth polarising beam splitters 22, 24, 26, 28 are configured to selectively direct photons in different directions based on the polarisation mode of the photons.

[0107] In an analogous manner to that described with reference to Figures 2 to 8, in the example of Figure 9, photons with a vertical polarisation mode incident at the first polarising beam splitter 22 from the first node 2 are directed from the first polarising beam splitter 22 to a first interference arrangement 30A. Photons with a horizontal polarisation mode incident on the first polarising beam splitter 22 are directed to a second interference arrangement 30B. Similarly, photons with a vertical polarisation mode incident at the second polarising beam splitter 24 from the second node 4 are directed from the second polarising beam splitter to the first interference arrangement 30A and photons with a horizontal polarisation mode incident on the second polarising beam splitter 24 are directed to the second interference arrangement 3 OB. Similarly, photons with a vertical polarisation mode incident at the third polarising beam splitter 26 from the third node 6 are directed to the first interference arrangement 30A and photons with a horizontal polarisation mode are directed to the second interference arrangement 30B. Similarly, photons with a vertical polarisation mode incident at the fourth polarising beam splitter 28 from the fourth node 8 are directed to the first interference arrangement 30 A and photons with a horizontal polarisation mode are directed to the second interference arrangement 30B. Whilst the first, second, third and fourth polarising beam splitters 22, 24, 26, 28 are shown to direct photons with a vertical polarisation to the first interference arrangement 30A and photons with a horizontal polarisation to the second interference arrangement 30B, in further examples additional, or alternative, transformations of polarisations of photons are implemented. For example, after separating polarisations into horizontal and vertical polarisation modes at the first, second, third and fourth polarising beam splitters 22, 24, 26, 28, horizontal and / or vertical polarisation modes of photons can be transformed such the polarisation modes of the photons entering each of the first and second interference arrangements 30A, 30B are the same. For example, the vertical polarisation modes of photons can be transformed to horizontal polarisation modes of photons. In order to transform the polarisation mode of photons in then entanglement apparatus 200, polarisation rotators (e.g., half-wave plates) may be used to transform photons exiting the polarising beam splitters 22, 24, 26, 28. For example, photons having a horizontal polarisation mode exiting each of the polarising beam splitters 22, 24, 26, 28 may be directed through a respective polarisation rotator before being input into the second interference arrangement 3 OB such that the second interference arrangement 3 OB receives photons having a vertical polarisation mode. In such an example, both the first and second interference arrangements 30 A, 3 OB are arranged to receive photons having the same vertical polarisation mode.

[0108] Beneficially, where each independent interference arrangement 30A, 30B is configured to interfere photons with the same polarisations, the same physical construction of the interference arrangements 30A, 30B can be implemented. This is particularly advantageous in photonic integrated circuits, where the same type of waveguides can be replicated for each interference arrangement 30 A, 3 OB, thereby providing efficiency in fabrication.

[0109] Accordingly, the quantum entanglement apparatus 900, comprises: a plurality of polarising beam splitters 22, 24, 26, 28 wherein each polarising beam splitter 22, 24, 26, 28 is arranged to: receive photons from a respective node of the plurality of nodes 2, 4, 6, 8; and direct received photons to the first interference arrangement 30A or the second interference arrangement 30B based on the polarisation of the received photons. The first interference arrangement 30A has four inputs provided by the optical paths from each of the first, second, third and fourth polarising beam splitters 22, 24, 26, 28 each input configured to receive photons with a first polarisation from a respective node 2, 4, 6, 8. Similarly, the second interference arrangement 3 OB has four inputs provided by the optical paths from each of the first, second, third and fourth polarising beam splitters 22, 24, 26, 28 each input configured to receive photons with a second polarisation from a respective node 2, 4, 6, 8.

[0110] The first interference arrangement 30A has four outputs. As shown at Figure 9, the first interference arrangement 30A has one output path from the first interference arrangement 30A directed to a first photon detector 42 A associated with the first interference arrangement 30 A, another output path from the first interference arrangement 30A directed to a second photon detector 42B associated with the first interference arrangement 30 A, yet another output path from the first interference arrangement 30A directed to a third photon detector 42C associated with the first interference arrangement 30A and yet another output path from the first interference arrangement 30A to a fourth photon detector 42D associated with the first interference arrangement 30 A.

[0111] Similarly, the second interference arrangement 3 OB has one output path directed from the second interference arrangement 3 OB to a first photon detector 44 A associated with the second interference arrangement 3 OB, another output path directed from the second interference arrangement 3 OB to a second photon detector 44B associated with the second interference arrangement 3 OB, yet another output path directed from the second interference arrangement 3 OB to a third photon detector 44C associated with the second interference arrangement 3 OB and yet another output path directed from the second interference arrangement 3 OB a fourth photon detector 44D associated with the second interference arrangement 3 OB.

[0112] Each of the first interference arrangement 30A and the second interference arrangement 3 OB of the quantum entanglement apparatus 900 of Figure 9 provides a network of paths from each input to each output, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs.

[0113] As shown at Figure 9, the network of paths of the first and second interference arrangements 30A, 30B each comprise: a first beam splitter 36A, 36B, configured to: receive photons from a first node 2 and a fourth node 8 of the plurality of nodes 2, 4, 6, 8; and direct received photons to one of two outputs of the first beam splitter 36 A, 36B with a predetermined probability; a second beam splitter 34A, 34B configured to: receive photons from a second node 4 and a third node 6 of the plurality of nodes 2, 4, 6, 8; and direct received photons to one of two outputs with a predetermined probability; a third beam splitter 38 A, 38B configured to: receive photons from an output of the first beam splitter 36A, 36B and an output of the second beam splitter 34A, 34B; and direct received photons to one of two outputs with a predetermined probability; a fourth beam splitter 39A, 39B configured to: receive photons from the other output of the first beam splitter 36A, 36B and the other output of the second beam splitter 34A, 34B; and direct the received photons to one of two outputs with a predetermined probability.

[0114] The two outputs of the third beam splitter 38A of the first interference arrangement 30A are directed to respective first and second photon detectors 42 A, 42B associated with the first interference arrangement 30 A. The two outputs of the fourth beam splitter 39A of the first interference arrangement 30A are directed to respective third and fourth photon detectors 42C, 42D associated with the first interference arrangement 30 A. The two outputs of the third beam splitter 38B of the second interference arrangement 3 OB are directed to respective first and second photon detectors 44A, 44B associated with the second interference arrangement 3 OB. The two outputs of the fourth beam splitter 39B of the second interference arrangement 3 OB are directed to respective third and fourth photon detectors 44C, 44D associated with the first interference arrangement 3 OB. With such arrangements, all of the inputs with a first polarisation from respective nodes 2, 4, 6, 8 of the plurality of nodes 2, 4, 6, 8 are provided with a pathway to each of the photon detectors 42 A, 42B, 42C, 42D associated with the first interference arrangement 30 A and all of the inputs with a second polarisation from respective nodes 2, 4, 6, 8 of the plurality of nodes 2, 4, 6, 8 are provided with a pathway to each of the photon detectors 44A, 44B, 44C, 44D associated with the second interference arrangement 3 OB.

[0115] In the example of the quantum entanglement apparatus 900 of Figure 9, the first and / or second interference arrangement comprises at least one beam splitter configured to direct received photons to one of two outputs with a predetermined probability, wherein the predetermined probability is 50% for each of the two outputs.

[0116] The quantum entanglement apparatuses described with reference to Figures 2 to 9 comprise a plurality of polarising beam splitters, wherein each polarising beam splitter is arranged to: receive photons from a respective node of the plurality of nodes; and direct received photons to the first interference arrangement or the second interference arrangement based on the polarisation of the received photons.

[0117] In an example, the polarising beam splitters form part of an integrated photonic circuit, such as an integrated photonic circuit comprising at least one interference arrangement 30A, 30B. In further examples, the polarising beam splitters are provided separately to the interference arrangements 30 A, 3 OB of the quantum entanglement apparatus. In an example, the interference arrangements 30 A, 30B are provided as part of a photonic integrated circuit and the polarising beam splitters are provided using bulk optical components in combination with the photonic integrated circuit. In an example, the polarising beam splitters are attachable to the photonic integrated circuit in any suitable manner in order to reduce optical path lengths and thereby reduce optical losses. Advantageously, whilst polarising beam splitters may be provided as bulk optical components, such components can be small enough (for example, with a footprint of the order of 1 mm2) for efficient integration at the inputs of a photonic integrated circuit (for example, with an area of the order of 1 cm2), even where integration of such components within a photonic integrated circuit itself is impractical.

[0118] Whilst the quantum entanglement apparatuses described with reference to Figures 2 to 9 are shown such that first and second interference arrangement 30 A, 30B comprises at least one beam splitter configured to direct received photons to one of two outputs with a predetermined probability, in further examples, alternatively, the first and / or second interference arrangement 30A, 30B comprises at least one beam splitter configured to direct received photons to one of two outputs with a predetermined probability. In further examples, the functionality of beam splitters is provided using any suitable alternative and / or additional component.

[0119] Whilst the beam splitters described with reference to Figure 2, for example, direct received photons to one of two outputs with a predetermined probability that is 50% for each of the two outputs, in further examples, beam splitters that are configured to direct received photons to one of two outputs with any suitable predetermined probability to provide the functionality described herein are implemented.

[0120] Optionally, the at least one beam splitter of the quantum entanglement apparatus described herein comprises two waveguides coupled at a coupling interface, wherein the coupling interface is arranged to transmit and reflect received photons in accordance with the predetermined probability. Advantageously, such beam splitters may be fabricated in photonic integrated circuits using known techniques. In further examples, the at least one beam splitter is implemented in any appropriate manner to enable entanglement, for example using bulk optical components.

[0121] The quantum entanglement apparatuses described with reference to Figures 2 to 9 are shown to comprise a plurality of single photon detectors, each single photon detector associated with a different respective output of the plurality of outputs of the first interference arrangement and the plurality of outputs of the second interference arrangement. Optionally, the plurality of single photon detectors is an integrated array of photon detectors. In such integrated arrays, different pixels of the array are used to detect photons from respective optical outputs of the interference arrangements 30 A, 3 OB, thereby beneficially enabling integrations with small scale photonic integrated circuits comprising interference arrangements 30A, 30B. In further examples, photon detectors form at least part of a photonic integrated circuit. Beneficially, interference arrangements 30 A, 3 OB and photon detectors are provided in a stable and compact manner.

[0122] Whilst the interference arrangements 30A, 30B described herein are illustrated schematically, it is understood that these are optionally provided such that the first and second interference arrangement form at least part of a photonic integrated circuit. Alternatively, or additionally, the first and / or second interference arrangement 30A, 30B comprises one or more optical fibres configured to direct photons receivable at the respective first and / or second interference arrangement to one of the plurality of outputs. The quantum entanglement apparatuses described herein comprise two or more nodes configured to generate an entangled atom-photon pair. In further examples, the quantum entanglement apparatuses alternatively and / or additionally receive photons from any suitable external source.

[0123] Whilst the quantum entanglement apparatuses described with reference to Figures 2 to 9 generate photons at two or more nodes, optionally, the two or more nodes are each configured to generate spatially distinct photons. For example, the two or more nodes are each configured to generate multiple entangled atom-photon pairs into spatially different modes. Advantageously, the generation of spatially distinct photons is scalable to generate M spatially distinct photons, thereby enabling an increase in the entanglement rate between nodes by a factor of M times.

[0124] In an example, the two or more nodes comprise ion traps and / or neutral atom traps. In examples, an ion trap and / or neutral atom trap each comprises two or more nodes. In further examples, additionally, or alternatively the two or more nodes comprise atomic clocks, quantum sensors, quantum memory nodes and / or quantum computers.

[0125] In an example, the quantum entanglement apparatuses described herein comprise at least one lens configured to direct photons from one or more respective nodes to the quantum entanglement apparatus. Alternatively, or additionally, the quantum entanglement apparatuses described herein comprise at least one optical resonator configured to direct photons from one or more respective nodes to the quantum entanglement apparatus. Alternatively, or additionally, photons emitted by nodes are collected directly by integrated optical components forming at least part of the quantum entanglement apparatus.

[0126] Advantageously, the configurations of quantum entanglement apparatus described herein with reference to Figures 2 to 9 enable improved devices for entanglement of multiple nodes compared with known devices.

[0127] An example of improved entanglement of multiple nodes is described with reference to Figures 10 and 11. For example, Figure 10 shows a schematic representation 1000 of the Bell state analyser 100 of Figure 1 configured to switch entanglement between four nodes 2, 4, 6, 8. Such Bell state analysers use bulk optics and are therefore unsuitable for scaling with high density. Further, in order to provide selective entanglement between different nodes 2, 4, 6, 8, fibre switching is required. As shown at Figure 10, a four node 2, 4, 6, 8 is provided. In the example of Figure 10, the nodes 2, 4, 6, 8 are ion traps configured to generate entangled photon-ion pairs. Photons generated by the nodes 2, 4, 6, 8 are coupled to a respective single mode fibre 1012, 1014, 1016, 1018 via a respective optical assembly 1002, 1004, 1006, 1008. The single mode fibres 1012, 1014, 1016, 1018 are coupled to a fibre switch 1010 that is configured selectively to route photons from the nodes 2, 4, 6, 8 to the Bell state analyser 100. In order to provide quantum entanglement between different nodes 2, 4, 6, 8, active optical switching components of the fibres switch 1000 are used. However, the use of active switching and bulk components make scaling such arrangements impractical.

[0128] In contrast, Figure 11 shows a schematic representation of an integrated quantum entanglement apparatus 1100 configured to switch entanglement between four nodes 2, 4, 6, 8 using a passive quantum entanglement apparatus, such as the quantum entanglement apparatus 900 described with reference to Figure 9. In the example of Figure 11, the quantum entanglement apparatus 900 is used to enable selective, reconfigurable, and, or, multiplexed entanglement between multiple nodes 2, 4, 6, 8. In the example of Figure 11, four ion trap nodes 2, 4, 6, 8 are shown. Each of the nodes 2, 4, 6, 8 are configured to generate spatially distinct photons. In such cases, the nodes may each generate multiple entangled atom-photon pairs into spatially different modes. Each node 2, 4, 6, 8 has a respective lens 1102, 1104, 1106, 1108. Generation of spatially distinct photons directed to the respective lens 1102, 1104, 1106, 1108 associated with each node 2, 4, 6, 8 enables directional control of the emission of photons from nodes 2, 4, 6, 8 into respective multicore optical fibres (or single core fibres in a fibre array) 1112, 1114, 1116, 1118. Such directional control is described in further detail with reference to Figure 12.

[0129] Figure 12 shows a schematic representation of a photon router apparatus 1200. The photon router apparatus 1200 shows in further detail how a lens is used to enable control of the destination of photons generated at a node. In the example of Figure 12, there is shown a node 2, which may be an ion trap node as described herein. There is shown a lens 1206 associated with the node 2 and a multi-core fibre 1208 coupled to the lens. When photons are generated at a first position 1210, they are focused to a first core of the multi-core fibre 1208 and routed to a first destination 1202. When photons are generated at a second position 1212, they are focused to a second core of the multi -core fibre 1208 and routed to a second destination 1206. In this manner, control of the generation of photons at a node 2 enables selective photon routing. Whilst a multi-core fibre 1208 is described with reference to Figure 12, in further examples, additionally or alternatively, an array of single core optical fibres provides analogous functionality.

[0130] In an example, the emitter (which is an ion in the case of an ion trap node), may be physically moved between the first position 1210 and the second position 1212 by ion shuttling. In a further example, the emitter may be physically moved, alternatively or additionally, between the first position 1210, second position 1212 and a third position 1214. In further examples, the node generates photons from neutral atoms and the neutral atoms are moved between the first position 1210 and the second position 1212 and / or third position 1214 using the optical tweezer technique. In further examples, multiple different ions and / or neural atoms or other emitters are used to generate photons at spatially distinct positions. In such cases, the nodes may each generate multiple entangled atom-photon pairs into spatially different modes. Whilst three positions 1210, 1212, 1214 of emitter are described with reference to Figure 12, in further examples any appropriate numbers of positions are used.

[0131] With reference to Figure 11, such generation of spatially distinct photons enables control of the input of photons into a quantum entanglement apparatus. Therefore, in order to switch entanglement between different ones of the nodes 2, 4, 6, 8, different inputs from the nodes 2, 4, 6, 8 can be provided to the quantum entanglement apparatus 900, in contrast to the arrangement of Figure 10, which requires optical fibre switching of inputs from the nodes 2, 4, 6, 8. Beneficially, the integrated quantum entanglement apparatus 1100 provides control of entanglement without the need of external optical switches. Beneficially, the integrated quantum entanglement apparatus 1100 also provides multiplexing of entanglement distribution between nodes. Figure 13 shows a schematic representation of an entanglement multiplexer apparatus 1300. There is shown a quantum entanglement multiplexer 1300 comprising a plurality of quantum entanglement apparatuses 1302 as described herein, wherein the plurality of quantum entanglement apparatuses 1302 is arranged to provide entanglement between two or more spatially distinct photons at each of the plurality of nodes 2, 4. In such cases, the nodes may each generate multiple entangled atom-photon pairs into spatially different modes.

[0132] The plurality of quantum entanglement apparatuses 1302 are configured to receive photons from multiple nodes 2, 4. In the example of Figure 13, there is shown a first node 2 configured to generate photons and a second node 4 configured to generate photons. Each of the first node 2 and the second node 4 are configured to generate spatially distinct photons, as described with reference to Figure 12, such that photons generated at a first position 1210A, 1210B are focused by a respective lens 1206 A to a first core of a respective multi-core fibre 1208 A, 2108B and photons generated at a second position 1212A, 1212B are focused by the respective lens 1206 A, 1206B to a second core of the respective multi-core fibre 1208 A, 1208B.

[0133] The use of multi-core fibres 1208A, 1208B enables spatially distinct photons at each of the nodes 2, 4 to be routed to different destinations. In the example of Figure 13, photons generated at a first position 1210A, of the first node 2 are directed to a first quantum entanglement apparatus of the plurality of quantum entanglement apparatuses 1302. In the example of Figure 13, the first quantum entanglement apparatus is a quantum entanglement apparatus 200 as described with reference to Figure 2, and is configured to entangle two nodes 2, 4. In the example of Figure 13, photons generated at a second position 1212A, of the first node 2 are directed to a second quantum entanglement apparatus of the plurality of quantum entanglement apparatuses 1302. In the example of Figure 13, the second quantum entanglement apparatus is a quantum entanglement apparatus 200 as described with reference to Figure 2, and is configured to entangle two nodes 2, 4.

[0134] Similarly, photons generated at a first position 1210B of the second node 4 are directed to the first quantum entanglement apparatus of the plurality of quantum entanglement apparatuses 1302 and photons generated at a second position 1212B of the second node 4 are directed to the second quantum entanglement apparatus of the plurality of quantum entanglement apparatus 1302. In such a way, the spatially distinct photons generated at each of the nodes 2, 4 may be entangled. Advantageously, control of the photons generated at the nodes 2, 4 enables multiplexing of signals between the nodes 2, 4. Whilst Figure 13 shows multi -core optical fibres 1208A, 1208B, in further examples, additionally or alternatively, arrays of single core optical fibres provide analogous functionality. Whilst Figure 13 shows an entanglement multiplexer apparatus 1302 configured to entangle two node 2, 4, in further examples the entanglement multiplexer apparatus 1302 is scalable to provide multiple routes of entanglement between more than two nodes. Advantageously, increasing the number “M” of entanglement paths enables the rate of entanglement between nodes 2, 4 to be increased by a factor of M.

[0135] Figure 14 shows a schematic representation of a double repeater apparatus 1400 which is an example of a quantum repeater comprising the quantum entanglement apparatuses described herein. In particular there is shown a first node 2 and a second node 4. The first node 2 and the second node 4 are coupled to respective multi -core optical fibres 1208 A, 1208B, as described with reference to Figures 12 and 13. Photons generated at a first position 1210A, 1210B of each respective node 2, 4 are routed by a respective lens 1206A, 1206B to a respective first single optical fibre of the multi-core optical fibre 1208A, 1208B associated with the node 2, 4. The photons are subsequently routed to a quantum entanglement apparatus. In the example of Figure 14, the quantum entanglement apparatus 200 is configured to entangle two nodes 2, 4, as described with reference to Figure 2.

[0136] Photons generated at a second position 1212A, 1212B of each respective node 2, 4 are routed by the respective lens 1206A, 1206B to a respective single optical fibre of the multi-core optical fibre 208A, 1208B associated with the node 2, 4. Through controlled generation of photons at the nodes 2, 4, entanglement between the nodes 2, 4 is provided such that the destination nodes 1202, 1204 also operate in an entangled state, thereby providing a quantum repeater that enables entangled communication over increased distances, thereby facilitating the expansion of quantum networks. Whilst schematic representations of optical pathways are shown at Figures 2 to 14, it will be understood that the optical pathways may be implemented in any appropriate way in accordance with the functionality described herein.

[0137] For example, whilst the interference arrangements 30A, 30B described with reference to Figures 2 to 14 may be static components that are engineered in order to enable quantum entanglement through the interference of photons input into the interference arrangements 30 A, 3 OB, in further examples the interference arrangements 30 A, 3 OB are dynamically reconfigurable, thereby to enable selective entanglement of photons input into the interference arrangements 30 A, 3 OB. For example, in a four-node system, such as the quantum entanglement apparatus 900 described with reference to Figure 9, the interference arrangements 30 A, 30B may be implemented in a photonic integrated circuit that is dynamically reconfigurable. In an example of a dynamically reconfigurable arrangement, all four nodes 2, 4, 6, 8 are optionally entangled in one go. Through the dynamic reconfiguration of the photonic integrated circuit, at least a subset of the same components of the interference arrangements 30 A, 30B is used selectively to alter the entanglement between the nodes 2, 4, 6, 8 of the quantum entanglement apparatus 900. In an example, selected subsets of the four nodes 2, 4, 6, 8 are entangled. For example, the first node 2 is entangled with the second node 4 and the third node 6 is entangled with the fourth node 8. In further examples, the use of dynamically reconfigurable interferometers as the first and second interference arrangements 30 A, 30B provides any appropriate combination of entangled nodes from possible subsets of nodes.

[0138] Beneficially, the quantum entanglement apparatus and methods described herein implement interference of photons in two separate interferometers, where photons are split based on their polarisation mode prior to interference, in contrast to the previous systems, which interfere photons before passing them through polarising beam splitters. The subsequent analysis of Bell states enables quantum entanglement to be heralded. Advantageously, the quantum entanglement apparatus described herein does not require two polarisation modes to travel together up to the PBS positions in the same spatial mode, as is seen in the standard Bell state analyser 100 shown at Figure 1. Beneficially, there is no requirement for a beam splitter that is polarisation agnostic to a high degree, with such polarisation agnostic beam splitters being difficult to implement and not readily available.

[0139] Further, advantageously, the quantum entanglement apparatus described with reference to Figures 2 to 14 may be implemented using photonic integrated circuits (PICs). Such PICs guarantee stable operations, compactness and reliability. Beneficially, these features provide advantages for scaling up the number of nodes of a quantum network and for deployability. Having two orthogonal polarisations travelling in the same photonic integrated waveguide is difficult and has not yet been demonstrated with the required fidelity. Further, neither photonic integrated polarising beam splitters nor photonic integrated polarisation-agnostic beam splitters have been demonstrated with the necessary specifications for providing known Bell state analysers in a photonic integrated circuit. Accordingly, known systems cannot be adapted to provide PICs to enable entanglement with high fidelity. The new quantum entanglement apparatus described with reference to Figures 2 to 14 not only achieves maximum unambiguous discrimination between Bell states achievable using linear optical elements and non number- resolved single photon detectors, but is also implementable using PICs in an elegant and compact manner.

[0140] Advantageously, whilst the new quantum entanglement apparatus described herein can be built with free-space optical components, standard optical fibre components or PICs, a requirement for relative pathlength stability between different optical paths makes implementation with photonic integrated circuits particularly appealing, photonic integrated circuits exhibit high path length stability. Furthermore, the quantum entanglement apparatus described herein with reference to Figures 2 to 14 enables construction of photonic integrated circuits Bell state analysers with current well-proven technology, allowing for stable, alignment-free, high-performance, compact and deployable Bell state analysers.

[0141] Further, advantageously, the quantum entanglement apparatus described here does not use active components such as optical switches. Moreover, the concept can be extended to entangle any number of nodes with significant benefits for distributed quantum computers, thereby allowing for the creation of all-to-all entanglement in one single go, instead of achieving the same using only pair-wise entanglement between nodes in a sequential way.

[0142] Advantageously, the quantum entanglement apparatus described herein may be provided as modular components. For example, the interference arrangements 30A, 30B may be provided as a modular component that can be used in combination with one or more modular photon detectors, one or more polarising beam splitting modules and / or two or more entangled photon-pair generating node modules. Beneficially, the interference arrangements 30A, 30B provided to interfere photons of different polarisations may be provided in a compact arrangement whilst conventional, bulkier components, such as polarising beam splitters can be provided more conveniently at an external location on a photonic integrated circuit chip, for example.

Claims

CLAIMS1. A quantum entanglement apparatus comprising: a first interference arrangement configured to receive photons with a first polarisation from a plurality of nodes; and a second interference arrangement configured to receive photons with a second polarisation from the plurality of nodes, wherein each of the first and second interference arrangements comprises: a plurality of inputs, each input configured to receive photons from a respective node of the plurality of nodes; a plurality of outputs; and a network of paths from each input to each output, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs, wherein the first and second interference arrangements are configured such that detection of photons at the outputs of the first and second interference arrangements enables entanglement between at least two nodes of the plurality of nodes.

2. The quantum entanglement apparatus according to claim 1, wherein the first and / or second interference arrangement comprises at least one beam splitter configured to direct received photons to one of two outputs with a predetermined probability.

3. The quantum entanglement apparatus according to claim 2, wherein the at least one beam splitter is configured to direct received photons to one of two outputs with a predetermined probability by implementing the Hong-Ou-Mandel effect.

4. The quantum entanglement apparatus according to claim 2 or claim 3, wherein the predetermined probability is 50% for each of the two outputs.

5. The quantum entanglement apparatus according to any of claims 2-4, wherein the at least one beam splitter comprises two waveguides coupled at a coupling interface, wherein the coupling interface is arranged to transmit and reflect received photons in accordance with the predetermined probability.

6. The quantum entanglement apparatus according to claim 1, comprising: a plurality of polarising beam splitters, wherein each polarising beam splitter is arranged to: receive photons from a respective node of the plurality of nodes; and direct received photons to the first interference arrangement or the second interference arrangement based on the polarisation of the received photons.

7. The quantum entanglement apparatus according to any preceding claim, wherein the first and second interference arrangements enable entanglement of three nodes or four nodes.

8. The quantum entanglement apparatus according to any of claims 1 to 6, wherein the first and second interference arrangements enable entanglement of any number of nodes up to 2nnodes, wherein n is any positive integer.

9. The quantum entanglement apparatus according to claim 8, wherein each of the first and second interference arrangements comprise:2ninputs, each input configured to receive photons from a respective node of the plurality of nodes;2noutputs; and n sub-networks of the network of paths, wherein each sub-network comprises 2n / 2 beam splitters.

10. The quantum entanglement apparatus according to claim 9, comprising a first subnetwork, wherein each beam splitter of the first sub-network is configured to: receive polarised light from a different pair of inputs of the 2ninputs; and provide a pair of outputs.

11. The quantum entanglement apparatus according to claim 10, wherein the n subnetworks are arranged in a sequence of i=l to n sub-networks, wherein the outputs of each ithsub-network provides inputs for the (i+l)thsub-network, from i=l to (n-1).

12. The quantum entanglement apparatus according to claim 11, wherein the 2n / 2 beam splitters of each ithsub-network are arranged in 2(n-1)groups, wherein each group is configured to mix inputs from a different two groups of the (i-l)thsub-network and provide outputs.

13. The quantum entanglement apparatus according to any preceding claim, wherein the network of paths of the first and second interference arrangements each comprise: a first beam splitter configured to: receive photons from a first node and a second node of the plurality of nodes; and direct received photons to one of two outputs of the first beam splitter with a predetermined probability; a second beam splitter configured to: receive photons from a third node of the plurality of nodes and an output of the first beam splitter; and direct received photons to one of two outputs with a predetermined probability; and a third beam splitter configured to: receive photons from the other output of the first beam splitter and an output of the second beam splitter; anddirect received photons to one of two outputs with a predetermined probability.

14. The quantum entanglement apparatus according to any of claims 1 to 6, wherein the network of paths of the first and second interference arrangements each comprise: a first beam splitter configured to: receive photons from a first node and a fourth node of the plurality of nodes; and direct received photons to one of two outputs of the first beam splitter with a predetermined probability; a second beam splitter configured to: receive photons from a second node and a third node of the plurality of nodes; and direct received photons to one of two outputs with a predetermined probability; a third beam splitter configured to: receive photons from an output of the first beam splitter and an output of the second beam splitter; and direct received photons to one of two outputs with a predetermined probability; a fourth beam splitter configured to: receive photons from the other output of the first beam splitter and the other output of the second beam splitter; and direct the received photons to one of two outputs with a predetermined probability.

15. The quantum entanglement apparatus according to any preceding claim comprising a plurality of single photon detectors, each single photon detector associated with a different respective output of the plurality of outputs of the first interference arrangement and the plurality of outputs of the second interference arrangement.

16. The quantum entanglement apparatus according to claim 15, wherein the plurality of single photon detectors is an integrated array of single photon detectors.

17. The quantum entanglement apparatus according to any preceding claim, wherein the first and second interference arrangement form at least part of a photonic integrated circuit.

18. The quantum entanglement apparatus according to any preceding claim, wherein the first and / or second interference arrangement comprises one or more optical fibres configured to direct photons receivable at the respective first and / or second interference arrangement to one of the plurality of outputs.

19. The quantum entanglement apparatus according to any preceding claim, comprising a controller.

20. The quantum entanglement apparatus according to any preceding claim, comprising a data processing device configured to: analyse detected photons to determine data; and send the determined data to the plurality of nodes.

21. The quantum entanglement apparatus according to any preceding claim, comprising two or more nodes configured to generate an entangled atom-photon pair.

22. The quantum entanglement apparatus according to claim 21, wherein the two or more nodes are each configured to generate spatially distinct photons.

23. The quantum entanglement apparatus according to claim 21 or claim 22, wherein the two or more nodes comprise atomic clocks, quantum sensors, quantum memory nodes and / or quantum computers.

24. The quantum entanglement apparatus according to any of claims 21 to 23, wherein the two or more nodes comprise ion traps and / or neutral atom traps.

25. The quantum entanglement apparatus according to any of claims 21 to 24, comprising at least one lens configured to direct photons from one or more respective nodes to the quantum entanglement apparatus.

26. The quantum entanglement apparatus according to any of claims 21 to 25, comprising at least one optical resonator configured to direct photons from one or more respective nodes to the quantum entanglement apparatus.

27. The quantum entanglement apparatus according to any preceding claim, wherein the first polarisation is orthogonal to the second polarisation.

28. A quantum repeater comprising the quantum entanglement apparatus according to any of claims 1 to 27.

29. A quantum entanglement multiplexer comprising a plurality of quantum entanglement apparatuses according to any of claims 1 to 27, wherein the plurality of quantum entanglement apparatuses is arranged to provide entanglement between two or more spatially distinct photons at each of the plurality of nodes.

30. A method of entangling a plurality of nodes, the method comprising: generating photons at each of a plurality of nodes; directing photons with a first polarisation to a first interference arrangement and photons with a second polarisation to a second interference arrangement; at the first interference arrangement,receiving photons with the first polarisation at each input of a plurality of inputs from a respective node of the plurality of nodes; and directing the received photons to one of a plurality of outputs through a network of paths, wherein the network of paths is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs; at the second interference arrangement, receiving photons with the second polarisation at each input of a plurality of inputs from a respective node of the plurality of nodes; and directing the received photons to one of a plurality of outputs through a network of paths that is arranged such that a photon received at any input of the plurality of inputs may interfere with a photon received at any other of the plurality of inputs on one of the paths to one of the outputs; detecting photons at the outputs of the first and second interference arrangements; analysing detected photons to determine data; and sending the determined data to the plurality of nodes, thereby to entangle at least two nodes of the plurality of nodes.

31. The method according to claim 30, comprising: generating one or more entangled atom-photon pair at each of two or more nodes.

32. The method according to claim 31, wherein generating one or more entangled atom-photon pair at one of the two or more modes comprises: trapping an ion or neutral atom; and exciting an electronic transition of the trapped ion or neutral atom, such that the subsequent decay generates an entangled atom-photon pair at the node.

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