Methods and apparatuses for quantum clock synchronization

Abstract

A method for synchronization between a transmitter (110) and a receiver (120), wherein the transmitter (110) comprises means for quantum measurement. The method performed by the transmitter (110) comprising obtaining (210) at least one synchronization quantum system, obtaining (220), based on the at least one synchronization quantum system and at least one first entangled quantum sub- system of at least one entangled quantum system, at least one first post- measurement quantum system, at least one second post-measurement quantum system and at least two post-measurement bits of data, and transmitting (230), to the receiver (120), the at least one second post-measurement quantum system along a first path (130). Further there is a receiver (120) related method, a transmitter (110) and a receiver (120).

Description

[0001] METHODS AND APPARATUSES FOR QUANTUM CLOCK SYNCHRONIZATION

[0002] TECHNICAL FIELD

[0003] The present disclosure relates to a transmitter, a receiver and methods performed by the transmitter and the receiver. Related computer programs and computer readable storage mediums are also disclosed.

[0004] BACKGROUND

[0005] Telecommunication networks are evolving to provide limitless connectivity and enable latency sensitive applications (augmented reality, cloud gaming etc.) through intelligent network platform. The intelligent network platform may rely on heterogenous compute accelerators in the edge to cloud continuum to meet diverse requirements of future applications.

[0006] Several problems related to telecommunication networks have been solved on quantum computers. Examples of such problems i) Fourier transforms ii) maximum likelihood based soft Multiple-Input Multiple-Output (MIMO) detection, iii) offloading user equipment (UE) specific tasks to edge computing servers, and iv) offloading UEs to micro base stations within a coverage area of a macro cell to improve the quality of service.

[0007] Multi-chip quantum processors using e.g., distributing quantum computing appear to have fewer cross talks between quantum systems compared to equivalently large single chip processors. In distributing quantum computing systems, smaller processors may do local computation and communicate either through classical or through quantum channels. Distributing quantum operations between two processors ideally need precisely synchronized clocks, and non-evolving entangled pairs.

[0008] Quantum teleportation is frequently used in distributed quantum computing due to its reliance on classical channels for real-time communication and its ability to achieve high fidelity in information transfer using entangled particle pairs. For quantum teleportation, the coherence with which qubits communicate is crucial. Quantum systems rely on stability of quantum information encoded into a qubit. When, for example, transmitting or teleporting a message qubit such as 0) + 1311), any small inaccuracy will lead to a different message than intended. Inaccuracies may arise due to quantum noise such as channel noise and quantum decoherence. A triplet state such as | cf)+) is commonly used for teleportation and other distributed quantum operations. However, the triplet state | cf)+) is non-stationary and evolves under an action of the natural Hamiltonian across two processors. When using the triplet state |cf)+), the teleportation procedure can yield inaccurate results if the clocks are not synchronized. To avoid this issue, it is necessary to time operations. However, it is difficult to always maintain precisely synchronized clocks, which may lead to inaccurate information transfer between the processors. Therefore, clock desynchronization is a common problem in distributed quantum systems that can prevent a successful execution of tasks such as quantum teleportation between multiple quantum processors.

[0009] Sergey Bravyi, et al. "The future of quantum computing with superconducting qubits." Journal of Applied Physics 132.16 (2022) relates to synchronizing a set of clocks by using Einstein synchronization (ES). Thereby, light signals are exchanged between two entities who are positioned near their respective clocks, wherein actual timing information must be transmitted between the entities over a channel.

[0010] Hosoya "Einstein synchronisation by quantum teleportation." Journal of Physics Communications 4.7 (2020) relates to a teleportation-based synchronization method using ES, wherein actual timing information is transmitted using quantum teleportation.

[0011] However, transmitting actual timing information between entities over a channel may lead to imperfections generally limiting an accuracy of a synchronization.

[0012] Therefore, to synchronize clocks between two entities, additional synchronization measures need to be implemented for decreasing inaccuracies.

[0013] SUMMARY An object of the invention is to enable improved synchronization, e.g., with respect to a first stopwatch comprised in a transmitter and a second stopwatch comprised in a receiver.

[0014] A first aspect of the invention relates to a method for synchronization between a transmitter and a receiver, wherein the transmitter comprises means for quantum measurement. The method performed by the transmitter comprises obtaining at least one synchronization quantum system, obtaining, based on the at least one synchronization quantum system and at least one first entangled quantum subsystem of at least one entangled quantum system, at least one first postmeasurement quantum system, at least one second post-measurement quantum system and at least two post-measurement bits of data, and transmitting, to the receiver, the at least one second post-measurement quantum system along a first path. Thereby, the transmitter is enabled to obtain a first and a second synchronized stopwatch.

[0015] A second aspect of the invention relates to a method for synchronization between a transmitter and a receiver, wherein the receiver comprises means for quantum measurement. The method performed by the receiver comprises receiving, from the transmitter along a first path, at least one second post-measurement quantum system, obtaining, a first information based on at least one second entangled quantum sub-system of at least one entangled quantum system, the first information indicating a first evolvement of at least one initial entangled quantum system of the at least one entangled quantum system, and obtaining a second information using the at least one second post-measurement quantum system, the second information indicating an evolvement of the at least one second post-measurement quantum system. Thereby, the receiver is enabled to obtain the second synchronized stopwatch.

[0016] A third aspect of the invention relates to a system for synchronization between a transmitter and a receiver, wherein the transmitter and the receiver comprise means for quantum measurement. The system comprises the transmitter and the receiver. The transmitter is configured to perform the method according to according to the first aspect or any embodiment of the first aspect, and the receiver is configured to perform the method according any the second aspect or any embodiment of the second aspect.

[0017] A fourth aspect of the invention relates to a transmitter comprising means for quantum measurement, whereby the transmitter is configured to obtain at least one synchronization quantum system, obtain, based on the at least one synchronization quantum system and at least one first entangled quantum sub-system of at least one entangled quantum system, at least one first post-measurement quantum system, at least one second post-measurement quantum system and at least two postmeasurement bits of data; and transmit, to a receiver, the at least one second postmeasurement quantum system along a first path.

[0018] A fifth aspect of the invention relates to a transmitter comprising means for quantum measurement, comprising processing circuitry and a computer readable storage medium, the computer readable storage medium containing instructions executable by the processing circuitry. The transmitter is configured to obtain at least one synchronization quantum system, obtain, based on the at least one synchronization quantum system and at least one first entangled quantum sub-system of at least one entangled quantum system, at least one first post-measurement quantum system, at least one second post-measurement quantum system and at least two postmeasurement bits of data, and transmit, to a receiver, the at least one second postmeasurement quantum system along a first path.

[0019] A sixth aspect of the invention relates to a receiver comprising means for quantum measurement, whereby the transmitter is configured to receive, from a transmitter along a first path, at least one second post-measurement quantum system, obtain, a first information based on at least one second entangled quantum sub-system of at least one entangled quantum system, the first information indicating a first evolvement of at least one initial entangled quantum system of the at least one entangled quantum system, and obtain a second information using the at least one second post-measurement quantum system, the second information indicating an evolvement of the at least one second post-measurement quantum system.

[0020] A seventh aspect of the invention relates to a receiver comprising means for quantum measurement, comprising processing circuitry and a computer readable storage medium, the computer readable storage medium containing instructions executable by the processing circuitry. The receiver is configured to receive, from a transmitter along a first path, at least one second post-measurement quantum system, obtain, a first information based on at least one second entangled quantum sub-system of at least one entangled quantum system, the first information indicating a first evolvement of at least one initial entangled quantum system of the at least one entangled quantum system, and obtain a second information using the at least one second post-measurement quantum system, the second information indicating an evolvement of the at least one second post-measurement quantum system.

[0021] An eighth aspect of the invention relates to a computer program comprising instructions which, when executed on processing circuitry of a transmitter, cause the processing circuitry of the transmitter to carry out the method according to the first aspect or any embodiment of the first aspect, and / or processing circuitry of a receiver, cause the processing circuitry of the receiver to carry out the method according to the second aspect or any embodiment of the second aspect.

[0022] A ninth aspect of the invention relates to a tangible, non-volatile computer readable medium comprising instructions that, when executed on processing circuitry of a transmitter, cause the processing circuitry of the transmitter to carry out the method according to the first aspect or any embodiment of the first aspect, and / or processing circuitry of a receiver, cause the processing circuitry of the receiver to carry out the method according to the second aspect or any embodiment of the second aspect.

[0023] BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a schematic diagram illustrating an example of an environment.

[0025] Figure 2 is a flowchart illustrating a method 200 performed by the transmitter.

[0026] Figure 3 is a flowchart illustrating a method 300 performed by the receiver.

[0027] Figures 4 is a flowchart illustrating exemplary embodiments of the method 200 and 300, performed by the transmitter and receiver. Figure 5 illustrates a schematic diagram illustrating first embodiment.

[0028] Figure 6 illustrates a block diagram illustrating an example of an environment.

[0029] Figure 7 illustrates a block diagram illustrating embodiments of the transmitter.

[0030] Figure 8 illustrates a block diagram illustrating embodiments of the receiver.

[0031] DETAILED DESCRIPTION

[0032] Figure 1 shows a schematic diagram illustrating an example of an environment in which embodiments presented herein can be applied. Figure 1 illustrates a transmitter 110 and a receiver 120. Figure 1 further illustrates a first path 130 and a second path 140 between the transmitter 110 and the receiver 120. The transmitter 110 is configured to perform a method 200 as described in the description relating to Figure 2. The transmitter 110 may comprise a first measurement block 111 capable to perform quantum measurements and a first communication block 112 capable to send or receive information via the first path 130 and the second path 140. The receiver 120 is configured to perform a method 300 as described in the description relating to Figure 3. The receiver 120 may comprise a second communication block 122, wherein the communication block 122 is capable of sending or receiving information via the first path 130 or the second path 140 and / or a second measurement block 121 capable of performing quantum measurements. The transmitter 110 may be a first processor and the receiver 120 may be a second processor. The first path 130 may be a quantum communication channel such as a bosonic channel, a photonic quantum channel, an entangled based channel, an optical fiber or a microwave interconnect. The first path 130 may enable transmission of at least one quantum system. The second path 140 may be a classical channel such as a communication based on e.g., Ethernet, optical fiber based communication, and / or wireless communications, e.g., Wi-Fi, and / or a cellular network corresponding to one or a combination of 5G cellular networks, LTE, LTE- advanced, UMTS, or any other current or future wireless network, such as a future 3GPP 6G network, satellite based communication. Optionally, a production block 113 may be a hardware based set-up comprised in the transmitter 111 enabling producing a quantum system. Alternatively, the production block 113 may not be comprised in the transmitter 110. The production block 113 may for example comprise a laser, crystal and a state sampler for producing a quantum system. Alternatively, the production block 113 enables producing the quantum system using, e.g., a four-wave mixing (FWM) system, a Quantum Dots based system, an Atomic Cascades based system, an Entanglement Swapping based system or any other hardware set-up system for producing a quantum system.

[0033] The transmitter 110 is configured to obtain at least one synchronization quantum system, obtain at least one first post-measurement quantum system, at least one second post-measurement quantum system and at least two post-measurement bits of data and transmit, to the receiver 120, the at least one second post-measurement quantum system along a first path 130. The receiver 120 is configured to receive from the transmitter 110 along the first path 130, the at least one second postmeasurement quantum system, obtain a first information, the first information indicating a first evolvement of at least one initial entangled quantum system of the at least one entangled quantum system. The receiver 120 is further configured to obtain a second information, the second information indicating an evolvement of the at least one second post-measurement quantum system, and obtain a third information indicating a second evolvement of the at least one initial entangled quantum system.

[0034] The solution presented herein addresses the above-mentioned challenges of enabling increased accuracy, when for example transmitting or teleporting, between two entities such as two processors or the transmitter 110 and the receiver 120.

[0035] Figure 2 is a flowchart illustrating a method 200 performed by the transmitter 110, as shown in Figure 1 and described in the text relating thereto.

[0036] The method 200 comprises a first step 210, as illustrated in Figure 2, which is obtaining at least one synchronization quantum system. The method further comprises, an obtaining step 220, the transmitter 110 obtains, based on the at least one synchronization quantum system and at least one first entangled quantum subsystem of at least one entangled quantum system, at least one first postmeasurement quantum system, at least one second post-measurement quantum system and at least two post-measurement bits of data. In a transmitting step 230, the transmitter 110 transmits to the receiver 120, the at least one second postmeasurement quantum system along the first path 130.

[0037] By obtaining 210 the at least one synchronization quantum system, the transmitter 110 is enabled to use the synchronization quantum system for obtaining the at least one first post-measurement quantum system and the at least one second postmeasurement quantum system. By obtaining 220, at least one first postmeasurement quantum system, at least one second post-measurement quantum system and at least two post-measurement bits of data, a first and a second synchronized stopwatch may be started, wherein the at least one first postmeasurement quantum system may be associated with the first synchronized stopwatch and the at least one second post-measurement quantum system may be associated with the second synchronized stopwatch. Further by obtaining 220, the transmitter 110 may be enabled to synchronize the first and the second synchronized stopwatch to each other. By transmitting 230 the transmitter 110 may be enabled to share the second synchronized stopwatch with the receiver 120, wherein the second synchronized stopwatch may stay synchronized to the first synchronized stopwatch after transmission.

[0038] A quantum system may refer to quantum-mechanical system such as an atom, a particle such as a photon or an electron, or a nuclear spin. The quantum system may exist in a quantum superposition of states 0 and 1 , using the property of the quantum system, such as a polarization degree of freedom or a spin. Thus, the quantum system may register a quantum bit such as a Qubit. The at least one quantum system may refer to more than one quantum systems or a higher dimensional quantum system.

[0039] The at least one synchronization quantum system (herein referred to as 1 0) may be at least one quantum system comprising any superposition of at least one quantum state, such as all states of the form ) |0), wherein , such as |I|J)= | i+) or |I|J)= | i-) .The at least one synchronization quantum system may correspond to one quantum system or a higher dimensional quantum system such as a tensor product of a number of quantum systems. Alternatively, the at least one synchronization quantum system may be at least one quantum system comprising a continuous bell state.

[0040] Obtaining 220 the at least one first post-measurement quantum system, the at least one second post-measurement quantum system and the at least two postmeasurement bits of data may comprise performing a joint measurement using the at least one synchronization quantum system and at least one first entangled quantum sub-system of the at least one entangled quantum system. Performing may be done by the first measurement block 111.

[0041] Alternatively, obtaining 220 may comprise receiving, from a third entity, the at least one first post-measurement quantum system, the at least one second postmeasurement quantum system and the at least two post-measurement bits of data. The third entity may be capable of performing the joint measurement.

[0042] The joint measurement may be a bell measurement or a bipartite quantum measurement. In case of the joint measurement being a bell measurement, the at least two post-measurement bits of data may be a two-bit classical result associated to one of four Bell states. In case of the joint measurement being the bipartite quantum measurement the at least two post-measurement bits of data may refer to more than two classical bits.

[0043] The at least one first post-measurement quantum system and the at least one second post-measurement quantum system may be at least one quantum system each comprising at least one quantum state in a maximum superposition. In an example, the at least one first post-measurement quantum system may be for initializing the first stopwatch and the at least one second post-measurement quantum system may be for initializing the second stopwatch.

[0044] The at least one first post-measurement quantum system and the at least one second post-measurement quantum system may be correlated and may both begin to evolve naturally at the same time as the joint measurement is performed.

[0045] Obtaining 220 the at least one first post-measurement quantum system, the at least one second post-measurement quantum system and the at least two postmeasurement bits of data may comprise starting the first and the second synchronized stopwatch. In an example, starting comprises initializing the first and the second synchronized stopwatch based on the at least one first postmeasurement quantum system and the at least one second post-measurement quantum system. Alternatively, the at least one first post-measurement quantum system and the at least one second post-measurement quantum system correspond to the first and the second synchronized stopwatch respectively. The first and second stopwatch may be synchronized due to the correlation between the at least one first post-measurement quantum system and the at least one second postmeasurement quantum system.

[0046] Transmitting 230, to the receiver 120, the at least one second post-measurement quantum system along the first path 130, may comprise transmitting via or using the first communication block 112.

[0047] Referring to figure 2, which illustrates an optional step 202 comprising obtaining the at least one entangled quantum system, wherein at least one initial entangled quantum system evolves into the at least one entangled quantum system. An optional step 204 comprises transmitting, to the receiver 120, at least one second entangled quantum sub-system of the at least one entangled quantum system along the first path 130. An optional step 222 comprises transmitting, to the receiver 120, the at least two post-measurement bits of data along the second path 140. An optional step 232 comprises obtaining a first phase using the at least one first postmeasurement quantum system.

[0048] The at least one first and second entangled quantum sub-system may correspond to each a half or a share of the at least one entangled quantum system. In an example the at least one first entangled quantum sub-system is a share of 0.6 to 0.8 of the at least one entangled quantum system, wherein the at least one second entangled quantum sub-system is a share of 0.4 to 0.2 of the at least one entangled quantum system respectively.

[0049] Transmitting 204 the at least one second entangled quantum sub-system may optionally be comprised in step 230. Alternatively, the at least one second entangled quantum sub-system may be transmitted before step 230. Transmitting 204 may optionally be performed by the first communication block 112. Transmitting 222 the at least two post-measurement bits of data along the second path 140 may optionally be performed by the first communication block 112.

[0050] Obtaining 232 may be performed recurrent after a predefined time period, wherein the at least one first post-measurement quantum system may have evolved naturally. In an example the at least one first post-measurement quantum system oscillates as a function of time. Obtaining 232 may optionally performed by the first measurement block 111. Obtaining 232 a first phase may optionally comprise performing a Hadamard measurement on the at least one first post-measurement quantum system. Performing a Hadamard measurement may comprise performing a Hadamard operation on the at least one first entangled quantum sub-system and measuring on the at least one first entangled quantum sub-system. By measuring, a probability distribution may be obtained indicating the first phase.

[0051] The first phase may indicate a first clock phase and / or a time evolvement of the at least one first post-measurement quantum system indicating a period of time and / or a value of evolvement between the obtaining step 220 (in Figure 2) of obtaining, by the transmitter 110, the at least one first post-measurement quantum system and / or a last Hadamard measurement of the at least one second post-measurement quantum system to the obtaining step 232.

[0052] Figure 3 is a flowchart illustrating a method 300 performed by the receiver 120, as shown in Figure 1 and described in the text relating thereto.

[0053] The method 300 comprises a first step 310, as illustrated in Figure 3, which is receiving 310, from the transmitter 110, along the first path 130, at least one second post-measurement quantum system. The method further comprises, an obtaining step 320, wherein the receiver 120 obtains a first information based on at least one second entangled quantum sub-system of at least one entangled quantum system the first information indicating a first evolvement of at least one initial entangled quantum system of the at least one entangled quantum system. A step 330 comprises obtaining a second information using the at least one second postmeasurement quantum system the second information indicating an evolvement of the at least one second post-measurement quantum system. Receiving 310 the at least one second post-measurement quantum system, may enable the receiver 120 to obtain the synchronized second stopwatch. The obtaining steps 320 to 330 may enable the receiver 120 to read out the synchronized second stopwatch.

[0054] Receiving 310 may optionally comprise receiving by the second communication block 122.

[0055] Receiving 310 may optionally comprise obtaining the second stopwatch, wherein the second stopwatch is synchronized with the first stopwatch.

[0056] Obtaining 320 a first information may comprise performing a Hadamard measurement on the at least one second entangled quantum sub-system.

[0057] The first information may indicate a phase and / or a first time evolvement of the at least one initial entangled quantum system indicating a period of time and / or a value of evolvement between generation of the at least one initial entangled quantum system to the at least one entangled quantum system to the obtaining step 320.

[0058] Obtaining 330 may be performed recurrent after the predefined time period, wherein the at least one second post-measurement quantum system may have evolved naturally. In an example the at least one second post-measurement quantum system oscillates as a function of time.

[0059] Obtaining 330 a second information and / or obtaining 320 may comprise performing a Hadamard measurement on the at least one second post-measurement quantum system and / or the at least one second post-measurement quantum system. Performing a Hadamard measurement may optionally comprise performing by the second measurement block 121. Performing a Hadamard measurement may comprise performing a Hadamard operation on the at least one second entangled quantum sub-system and / or the at least one second post-measurement quantum system and measuring on the at least one second entangled quantum sub-system and / or the at least one second post-measurement quantum system. By measuring, a probability distribution may be obtained indicating the first information and / or the second information. The second information may indicate a second phase such as a second clock phase and / or a time evolvement of the at least one second post-measurement quantum system indicating a period of time and / or a value of evolvement between the obtaining step 220 (in Figure 2) of obtaining, by the transmitter 110, the at least one second post-measurement quantum system and / or last Hadamard measurement of the at least one second post-measurement quantum system to the obtaining step 330.

[0060] The third information may indicate a phase and / or a second time evolvement of the least one initial entangled quantum system indicating a period of time and / or a value of evolvement between generation of the at least one initial entangled quantum system to the obtaining step 220 (in Figure 2) of obtaining, by the transmitter 110, the at least one first post-measurement quantum system and at least one second post-measurement quantum system.

[0061] Referring to figure 3, which illustrates an optional step 302, which comprises receiving, from the transmitter 110 along the first path 130, the at least one second entangled quantum sub-system. An optional step 304 comprises receiving, from the transmitter 110 along a second path 140, at least two first post-measurement bits of data. An optional step 306 comprises based upon the at least two first postmeasurement bits of data, performing a quantum operation on the at least one second entangled quantum sub-system. An optional step 332 comprises obtaining, based on the first information and the second information, the third information indicating a second evolvement of the at least one initial entangled quantum system.

[0062] Receiving 302 and / or receiving 304 may comprise receiving by the second communication block 122. Optionally the step 302 is comprised in step 310.

[0063] The quantum operation may be a unitary operation such as a rotational operation. In a more detailed example, the quantum operation may be the rotational operation such as a Pauli-Z or Pauli-X operation.

[0064] Obtaining 332 the third information may optionally comprise calculating or determining the third information using the first information and the second information. The obtaining step 332 may enable more precise future transmissions. Figures 4 is a flowchart illustrating exemplary embodiments of the method 200 and 300, performed by the transmitter 110 and receiver 120, as shown in Figure 2 and Figure 3. Figure 4 refers to the transmitter 110 and the receiver 120 as shown in Figure 1 and described in the text relating thereto.

[0065] In an example, a phase reference is shared between the transmitter 110 and the receiver 120 prior to the steps described below. In the example a shared reference allows the transmitter 110 and the receiver 120 to agree on the orientation of their Block spheres. If the transmitter 110 and the receiver 120 do not share the phase reference, then the receiver 120 may interpret the synchronization particle |0) with an error.

[0066] Referring to Figure 4, in an optional step 402, the transmitter 110, obtains the at least one entangled quantum system (referred herein to as 10)evoi. ) Step 402 may correspond to step 202 of method 200. Obtaining 402 may comprise receiving the at least one entangled quantum system from a third entity. Alternatively obtaining 202 may comprise preparing the at least one initial entangled quantum system (herein referred to as 10)). Preparing the at least one initial entangled quantum system 1 ) may comprise producing the at least one initial entangled quantum system | ) using the production block 113. Alternatively, any other hardware system may be used suitable to prepare at least one initial entangled quantum system |0).

[0067] In an example the at least one initial entangled quantum system |0) may correspond to a triplet state such as a Bell state. In an example the at least one initial entangled quantum system |0) evolves naturally into the at least one entangled quantum system 10)evoi. , wherein the at least one entangled quantum system may comprise the third information (referred herein to as ). Alternatively, the at least one initial entangled quantum system may refer to a to a bipartite entangled state such as a GHZ state or W state for example.

[0068] An optional step 404 comprises, transmitting, by the transmitter 110 to the receiver 120, the at least one second entangled quantum sub-system (referred herein to as 1 ) B ) of the at least one entangled quantum system |0)evoi. along the first path 130. The optional step 404 further comprises receiving, by the receiver 120 from the transmitter 110, along the first path 130, the at least one second entangled quantum sub-system |0) B ■ Step 404 may correspond to step 204 of method 200 and to step 302 of method 300.

[0069] In a step 406, the transmitter 110, obtains the at least one synchronization quantum system (referred herein to as |0)). The Step 406 may correspond to step 210 of method 200. Obtaining 406 the at least one synchronization quantum system 10) may comprise encoding the superposition state onto a quantum system or preparing the at least one synchronization quantum system |0). Alternatively, obtaining 406 may comprise receiving the at least one synchronization quantum system |0) from a third entity.

[0070] In a step 408, the transmitter 110, obtains at least one first post-measurement quantum system (referred herein to at least one second post-measurement quantum system (referred herein to ) and at least one two-post measurement bits of data. The step 408 may correspond to the step 220 of method 200.

[0071] An optional step 410, comprises transmitting, by the transmitter 110 to the receiver 120, the at least two-post measurement bits along the second path 140. The step 410 further comprises receiving, by the receiver 120 from the transmitter 110, along the second path 140, at least two first post-measurement bits of data. The step 410 may correspond to the step 222 of method 200 and to the step 304 of method 300.

[0072] In an optional step 412, the receiver 120 performs, based upon the at least two first post-measurement bits of data, a quantum operation on the at least one second entangled quantum sub-system. The step 412 may correspond to the step 306 of method 300. Performing 412 may comprise correcting an energy eigen basis and the first information such as the phase of the at least one second entangled quantum sub-system |0) B ■ A step 414 comprises, transmitting, by the transmitter 110 to the receiver 120, the at least one second post-measurement quantum system |v>2 along the first path 130. The step 414 further comprises receiving, by the receiver 120 from the transmitter 110, along the first path 130, the at least one second post-measurement quantum system |v>2 ■ The step 414 may correspond to the step 230 of method 200 and to the step 310 of method 300. In an example, the step 414 is performed before step 410 or step 412.

[0073] An optional step 416 comprises, obtaining, by the transmitter 110, a first phase using the at least one first post-measurement quantum system . The step 416 may correspond to the step 232 of method 200. In an example, step 416 may be performed before any of the steps 410 to 414.

[0074] A step 418 comprises, obtaining, by the receiver 120, the first information (may be referred herein to ( + 0)) based on the at least one second entangled quantum sub-system The step 418 may correspond to the step 320 of method 300.

[0075] A step 420 comprises, obtaining, by the receiver 120, the second information (referred herein to 6) using the at least one second post-measurement quantum system | v) 2 ■ The step 420 may correspond to the step 330 of method 300. In an example the step 420 may be performed before step 418 or step 416.

[0076] An optional step 422 comprises, obtaining, by the receiver 120, based on the first information ( + 0) and the second information 6, the third information The step 422 may correspond to the step 332 of method 300. In an example the third information may be calculated with = ( + 0) - 6.

[0077] A Figure 5 illustrates a schematic diagram illustrating a first embodiment of the steps described with reference to Figure 4 and the methods 200 and 300, performed by the transmitter 110 and receiver 120. Figure 5 refers to the transmitter 110, the receiver 120, the first measurement block 111 , the second measurement block 121 , the first communication block 112 and the second communication block 122 as shown in Figure 1 and described in the text relating thereto. Further, Figure 5 refers to a first part of the first communication block 512 and a first part of the second communication block 522 capable of transmitting and receiving via the second path 140, and a second part of the first communication block 514 and a second part of the second communication block 524 capable of transmitting and receiving via the first path 130.

[0078] The first embodiment may comprise performing the step 402, wherein the transmitter 110 prepares an initial entangled quantum system 1 ), being a Bell triplet state

[0079] 1 such as a |+) pair, wherein the |+) pair corresponds to |0+)= ~^ (

[0080] 100)+ 111)). The initial entangled quantum system naturally evolves into an entangled quantum system pair | )evoi, wherein | )evol. — |00)+e^|ll)).

[0081] The first embodiment may further comprise performing the step 404 as showed in Figure 5, wherein the transmitter 110 transmits a second entangled quantum sub system, wherein the second entangled quantum sub system is a first half of the |+) pair referred herein as |+) g and the second entangled quantum subsystem is transmitted via the second part of the first communication block 514 to the second part of the second communication block 524 via the first path 130.

[0082] Figure 5 further refers to performing the step 406, wherein the synchronization quantum system prepared by the transmitter 110 and corresponds to I0)=l+).

[0083] The first embodiment may further comprise performing the step 408, wherein a Bell measurement is performed using a first entangled quantum sub-system, wherein the first entangled quantum sub-system is a second half of the pair referred herein as the synchronization quantum system |I|J). The Bell measurement is performed via the first measurement block 111. The transmitter 110 may thus obtain a first post-measurement quantum system and a second post-measurement quantum system in maximum superposition each and two post-measurement bits (referred herein to as bgbj corresponding to one of the four Bell states bgbi= 00, 01 , 10, or 11 .

[0084] The first embodiment comprises performing step 410 as shown in Figure 5, wherein the two-post measurement bits of data bgb^ are sent via the second path 140 via the first part of the first communication block 512 and received by the first part of the second communication block 522.

[0085] The first embodiment comprises performing step 412, wherein the receiver 120 performs a Pauli-Z rotation or a Pauli-X rotation on the second entangled quantum sub-system based on the two post-measurement bits of data bgb^. In case bg is to 1 , the receiver 120 performs a Pauli-Z rotation. In case b^ is 1 , the receiver 120 performs a Pauli-X rotation. In case bgand b^ is 1 the receiver performed a Pauli-Z and Pauli-X rotation. Thus, no rotation if performed if bg and b^ are 0. Step 412 may be performed by the second measurement block 121 . After rotation the receiver 120 obtains a rotated second entangled sub-system, referred herein to as B r- wherein

[0086] The first embodiment further comprises performing step 414 as shown in Figure 5, wherein the transmitter 110 transmits the second post measurement quantum system | v>2 , wherein the second part of the first communication block 514 may sent the second post measurement quantum system |v>2 via the first path 130 and the second part of the second part of the first communication block 524 may receive the second post measurement quantum system | v>2 ■

[0087] The first embodiment further comprises performing step 416, wherein the transmitter 110 performs a Hadamard measurement on the first post measurement quantum system . The transmitter 110 may perform step 416 recurrently in a predefined first frequency. In case the transmitter 110 performs step 416 for the first time, the first phase indicates the time period since the Bell measurement. In case the transmitter 110 performed step 416 recurrent the first phase indicates the last measurement of the first post measurement quantum system |v)i. This way the transmitter 110 may use |v)i as the first synchronized stopwatch.

[0088] The first embodiment further comprises performing step 418, wherein to obtain the first information ( + 0), the receiver 120 performs a Hadamard measurement on the rotated second entangled sub-system |1) ). The measurement may be performed via the second measurement block 121.

[0089] The first embodiment further comprises performing step 420, wherein to obtain the second information 6, the receiver 120 performs a Hadamard measurement on the second post measurement quantum system | v>2 ■ The receiver 120 may perform step 420 recurrently in predefined second frequency, e.g., similar or different to the predefined first frequency. In case the receiver 120 performs step 420 for the first time, the second information indicates the time period passed since the Bell measurement. In case the receiver 120 performed step 420 recurrent the second information indicates the last measurement of the second post measurement quantum system | v>2 ■ This way the receiver 120 may use as the second synchronized stopwatch.

[0090] The first embodiment comprises performing step 422, wherein the third indication is calculated using the first information ( + 0) and the second information 6.

[0091] Referring to Figure 4, a second embodiment comprises performing steps 402 to 422 as described in the first embodiment, wherein the initial entangled quantum system 1 ), being any other Bell triplet state and the synchronization particle |I|J) being any superposition of at least one quantum state.

[0092] A third embodiment may comprise performing steps 402 to 422, wherein the at least one initial entangled quantum system, the at least one synchronization particle refers to more than one initial entangled quantum system. In the third embodiment step 408 may comprise performing the bipartite quantum measurement, wherein more than one first post-measurement quantum systems, more than one second post-measurement quantum systems and more than two-post measurement bits of data are obtained by the transmitter 110.

[0093] In an embodiment, the transmitter 110 and the receiver 120 are part of at least one of a quantum teleportation system, a quantum key distribution system; a superdense coding system, a Quantum Secure Direct Communication (QSDC) system, a Quantum Oblivious Transfer, QOT, system, a Quantum Anonymous Voting system, a Quantum Bit Commitment system, a Quantum Secret Sharing system, a Quantum Authentication system, a Quantum Secure Multi-Party Computation system, a Quantum Private Information Retrieval system, a Quantum Metrology and Sensing system, a Quantum Joint Communication and sensing system, or at least one data center. In an example the at least one data center is at least one single data center enclosure wherein reference frames between two systems are synchronized and the first, second clock and a third clock synchronized to the first and second clock using method 200 and 300 is comprised in each of the enclosures. In an example method 200 and 300 may be performed by the transmitter 110 and receiver 120 being any two processors in a multi-chip quantum computer without prior clock synchronization.

[0094] In the following an example is described wherein the method 200 and 300 can be applied to. In the example, the steps 402 to 422 may be performed in a quantum teleportation system environment.

[0095] In the example the transmitter 110 may additionally obtain a message quantum system and perform a joint measurement using the message quantum system and at least one first entangled quantum sub-system of at least one second entangled quantum system. Upon performing the second joint measurement, the transmitter 110 may obtain at least two second post-measurement bits of data and may transmit to the receiver 120 at least one second entangled quantum sub-system of the at least one second entangled quantum system along the first path 130. The transmitter 110 may further transmit to the receiver 120, the at least two second postmeasurement bits of data along the second path 140.

[0096] In the example, the message quantum system, referred herein to may be a quantum system wherein information is decoded to in e.g., the form | i|i2 )= a 10) + P 11) , wherein a and p are real numbers. The at least one second entangled quantum system may correspond to at least one triplet state such as a Bell state, which has naturally evolved. Alternatively, the at least one second entangled quantum system may refer to a bipartite entangled state such as a GHZ state or W state for example. In case of the joint measurement being a bell measurement, the at least two second post-measurement bits of data may be the two-bit classical result associated to one of four Bell states. In case of the joint measurement being the bipartite quantum measurement more the at least two second post-measurement bits of data may refer to more than two classical bit results.

[0097] In the example the receiver 120 may additionally receive from the transmitter 110, the at least one second entangled quantum sub-system of the at least one second entangled quantum system along the first path 130 and receive, from the transmitter 110, the at least two second post-measurement bits of data along the second path 140. Based on the at least two second post-measurement bits of data, the receiver 120 may perform a quantum operation on the at least one second entangled quantum sub-system of the at least one second entangled quantum system. The transmitter 110 may obtain the message quantum system, by applying the third information and the second information to the at least one second entangled quantum sub-system of the at least one second entangled quantum system. By applying, the transmitter 110 may be enabled to obtain precisely the message quantum system taking effects leading to imprecise transmission like channel noise and quantum decoherence into account.

[0098] In the example synchronization and teleportation may be performed with the same hardware settings, e.g., no changes to the state sampler 115, and architecture without requirement for a modification, which enables reduction of costs of hardware resources, avoiding latency attached to software modification of hardware configurations of the quantum teleportation system. The same hardware settings prevent costly and erratic frequent switching, improving the fidelity of synchronization and teleportation. Figure 6 illustrates a block diagram illustrating an example of an environment wherein the method 200 and 300 could be applied to. Figure 6 illustrates an infrastructure for a cloud implementation scenario of a data center, wherein the transmitter 110 and the receiver 120 is comprises for example in a Kubernetes cluster node such as a K8s Cluster Node x. The transmitter 110 and the receiver 120 may be two quantum processing units (QPll)-x and may share a direct quantum link being the first path 130. An application quantum circuit is passed through from an application POD 604 to a distributed quantum orchestrator 606 to transpile the application quantum circuit to the multi-qubits system of the data center. The application quantum circuit is passed further to the quantum execution manager 608, which may utilize an interconnect driver 610 to send microwave control, receive readout signals and / or provide classical information transfer between the transmitter 110 and receiver 120 such as the second path 140. The transmitter 110 and receiver 120 comprising a Quantum Memory 612 for entanglement storage, 616 each and a Quantum Execution Unit 614, 618 each.

[0099] Figure 7 illustrates a block diagram illustrating embodiments of the transmitter 110 in further detail. In practice, the steps 202 to 232 of the method 200 performed by the transmitter 110 are performed by processing circuitry 704, embodied in one or more processors and / or microprocessors arranged to execute a computer program 701 that is downloaded to a computer program product 705, here in the form of a suitable computer readable storage medium 702 associated with the microprocessor. The computer readable storage medium 702 may be a memory, such as a random access memory (RAM) or a read-only memory (ROM), or a tangible non-volatile computer readable storage medium, such as flash memory or a hard disk drive, or any combination thereof. The computer program 701 comprises computerexecutable instructions stored or downloaded to the computer readable storage medium 702 and are executable by the processing circuitry 704. Alternatively, the computer program 701 may be transferred to the computer readable storage medium 702 using a suitable computer program product, such as a memory stick or in a memory of a device. Thus, the computer program 701 may be stored in any suitable manner in the computer program product. The processing circuity 704 is arranged to cause the transmitter 110 to carry out the steps 202 to 232 of method 200 in accordance with any of the of the described embodiments for steps 202 to 232. The processing circuitry 704 is in one embodiment one or more general- purpose processors wherein each one of the general purpose processors includes one or more cores, but may alternatively be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a complex programmable logic device (CPLD), etc. An I / O interface 703 is provided for communicating with external and / or internal entities using wired communications, e.g., based on Ethernet, and / or wireless communications, e.g., WiFi, and / or a cellular network corresponding to one or a combination of 5G cellular networks, LTE, LTE-advanced, UMTS, or any other current or future wireless network, such as a future 3GPP 6G network, as long as the principles described below are applicable.

[0100] Figure 8 illustrates a block diagram illustrating embodiments of the receiver 120 in further detail. In practice, the steps 302 to 332 of the method 300 performed by the receiver 120 are performed by processing circuitry 804, embodied in one or more processors and / or microprocessors arranged to execute a computer program 801 that is downloaded to a computer program product 805, here in the form of a suitable computer readable storage medium 802 associated with the microprocessor. The computer readable storage medium 802 may be a memory, such as a random access memory (RAM) or a read-only memory (ROM), or a tangible non-volatile computer readable storage medium, such as flash memory or a hard disk drive, or any combination thereof. The computer program 801 comprises computerexecutable instructions stored or downloaded to the computer readable storage medium 802 and are executable by the processing circuitry 804. Alternatively, the computer program 801 may be transferred to the computer readable storage medium 802 using a suitable computer program product, such as a memory stick or in a memory of a device. Thus, the computer program 801 may be stored in any suitable manner in the computer program product. The processing circuity 804 is arranged to cause the receiver 120 to carry out the steps 302 to 332 of method 300 in accordance with any of the of the described embodiments for steps 302 to 332. The processing circuitry 804 is in one embodiment one or more general-purpose processors wherein each one of the general purpose processors includes one or more cores, but may alternatively be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a complex programmable logic device (CPLD), etc. An I / O interface 803 is provided for communicating with external and / or internal entities using wired communications, e.g., based on Ethernet, and / or wireless communications, e.g., Wi-Fi, and / or a cellular network corresponding to one or a combination of 5G cellular networks, LTE, LTE-advanced, UMTS, or any other current or future wireless network, such as a future 3GPP 6G network, as long as the principles described below are applicable.

Claims

CLAIMS1 . A method for synchronization between a transmitter (110) and a receiver (120), wherein the transmitter (110) comprises means for quantum measurement, the method performed by the transmitter (110) comprising: obtaining (210) at least one synchronization quantum system: obtaining (220), based on the at least one synchronization quantum system and at least one first entangled quantum sub-system of at least one entangled quantum system, at least one first post-measurement quantum system, at least one second post-measurement quantum system and at least two post-measurement bits of data; and transmitting (230), to the receiver (120), the at least one second postmeasurement quantum system along a first path (130).

2. The method according to claim 1 , wherein the method comprises: obtaining (232) a first phase using the at least one first postmeasurement quantum system.

3. The method according to claim 02, wherein obtaining (232) the first phase comprises: performing a Hadamard measurement on the at least one first postmeasurement quantum system.

4. The method according to any of the previous claims, wherein the method comprises: obtaining (202) the at least one entangled quantum system, wherein at least one initial entangled quantum system evolves into the at least one entangled quantum system.

5. The method according to any of the previous claims, wherein the method comprises: transmitting (204), to the receiver (120), at least one second entangled quantum sub-system of the at least one entangled quantum system along the first path (130).

6. The method according to any of the previous claims, wherein the method comprises: transmitting (222), to the receiver (120), the at least two postmeasurement bits of data along a second path (140).

7. The method according to any of the previous claims, wherein the transmitter (110) and the receiver (120) are part of at least one of a quantum teleportation system; a quantum key distribution system; a superdense coding system; a Quantum Secure Direct Communication, QSDC, system; a Quantum Oblivious Transfer, QOT, system; a Quantum Anonymous Voting system; a Quantum Bit Commitment system; a Quantum Secret Sharing system; a Quantum Authentication system; a Quantum Secure Multi-Party Computation system; a Quantum Private Information Retrieval system; a Quantum Metrology and Sensing system; a Quantum Joint Communication and sensing system; orat least one data center.

8. The method according to any of the previous claims, wherein obtaining (220) the at least one first post-measurement quantum system, the at least one second post-measurement quantum system and the at least two postmeasurement bits of data comprises: performing a joint measurement using the at least one synchronization quantum system and at least one first entangled quantum sub-system of the at least one entangled quantum system.

9. The method according to any of the previous claims, wherein obtaining (220) the at least one first post-measurement quantum system, the at least one second post-measurement quantum system and the at least two postmeasurement bits of data comprises starting a first and a second synchronized stopwatch.

10. The method according to any of the previous claims, wherein the at least one first post-measurement quantum system and the at least one second postmeasurement quantum system are correlated.11 . The method according to any of the previous claims, wherein the at least one synchronization quantum system comprises a superposition of at least one quantum state12. The method according to any of the previous claims, wherein the at least one entangled quantum system is a triplet quantum system.

13. A method for synchronization between a transmitter (110) and a receiver (120), wherein the receiver (120) comprises means for quantum measurement, the method performed by the receiver (120) comprising: receiving (310), from the transmitter (110) along a first path (130), at least one second post-measurement quantum system;obtaining (320), a first information based on at least one second entangled quantum sub-system of at least one entangled quantum system, the information indicating a first evolvement of at least one initial entangled quantum system of the at least one entangled quantum system; and obtaining (330) a second information using the at least one second post-measurement quantum system, the second information indicating an evolvement of the at least one second post-measurement quantum system.

14. The method according to claim 13, wherein the method comprises: obtaining (332), based on the first information and the second information, a third information indicating a second evolvement of the at least one initial entangled quantum system.

15. The method according to any of claims 13 to 14, wherein the method comprises: receiving (302), from the transmitter (110) along the first path (130), the at least one second entangled quantum sub-system.

16. The method according to any of claims 13 to 15, wherein the method comprises: receiving (304), from the transmitter (110) along a second path (140), at least two first post-measurement bits of data; based upon the at least two first post-measurement bits of data, performing (306) a quantum operation on the at least one second entangled quantum sub-system.

17. The method according to any of claims 13 to 16, wherein the transmitter (110) and the receiver (120) are part of at least one of a quantum teleportation system; a quantum key distribution system;a superdense coding system; a Quantum Secure Direct Communication, QSDC, system; a Quantum Oblivious Transfer, QOT, system; a Quantum Anonymous Voting system; a Quantum Bit Commitment system; a Quantum Secret Sharing system; a Quantum Authentication system; a Quantum Secure Multi-Party Computation system; a Quantum Private Information Retrieval system; a Quantum Metrology and Sensing system; a Quantum Joint Communication and sensing system; or at least one data center.

18. The method according to any of claims 13 to 17, wherein obtaining (320) the second information comprises: performing a Hadamard measurement on the at least one second postmeasurement quantum system.

19. The method according to any of claims 13 to 18, wherein obtaining (310) the first information comprises: performing a Hadamard measurement on the at least one second entangled quantum sub-system.

20. The method according to any of claims 13 to 19, wherein receiving (310) the at least one second post-measurement quantum system comprises obtaining a second stopwatch, wherein the second stopwatch is synchronized with afirst stopwatch.21 . The method according to any of claims 13 to 20, wherein the at least one second post-measurement quantum system at least one first postmeasurement quantum system are correlated.

22. The method according to any of claims 13 to 21 , wherein the at least one entangled quantum system is a triplet quantum system.

23. A system for synchronization between a transmitter (110) and a receiver (120), wherein the transmitter (110) and the receiver (120) comprise means for quantum measurement, the system comprising the transmitter (110) and the receiver (120), the transmitter (110) is configured to perform the method according to any of claims 1 to 12; and the receiver (120) is configured to perform the method according any of claims 13 to 22.

24. A transmitter (110) comprising means for quantum measurement, whereby the transmitter (110) is configured to: obtain at least one synchronization quantum system: obtain, based on the at least one synchronization quantum system and at least one first entangled quantum sub-system of at least one entangled quantum system, at least one first post-measurement quantum system, at least one second post-measurement quantum system and at least two post-measurement bits of data; and transmit, to a receiver (120), the at least one second postmeasurement quantum system along a first path (130).

25. The transmitter (110) according to claim 24, configured to perform the method according to any of claims 02 to 12.

26. A transmitter (110) comprising means for quantum measurement, comprising processing circuitry (704) and a computer readable storage medium (702), the computer readable storage medium (702) containing instructions executable by the processing circuitry (704), whereby the transmitter (110) is configured to: obtain at least one synchronization quantum system; obtain, based on the at least one synchronization quantum system and at least one first entangled quantum sub-system of at least one entangled quantum system, at least one first post-measurement quantum system, at least one second post-measurement quantum system and at least two post-measurement bits of data; and transmit, to a receiver (120), the at least one second postmeasurement quantum system along a first path (130).

27. The transmitter (110) according to claim 26, configured to perform the method according to any of claims 02 to 12.

28. A receiver (120) comprising means for quantum measurement, whereby the transmitter (110) is configured to: receive, from a transmitter (110) along a first path (130), at least one second post-measurement quantum system; obtain, a first information based on at least one second entangled quantum sub-system of at least one entangled quantum system, the first information indicating a first evolvement of at least one initial entangled quantum system of the at least one entangled quantum system;obtain a second information using the at least one second postmeasurement quantum system, the second information indicating an evolvement of the at least one second post-measurement quantum system.

29. The receiver (120) according to claim 28, configured to perform the method according to any of claims 15 to 22.

30. A receiver (120) comprising means for quantum measurement, comprising processing circuitry (804) and a computer readable storage medium (802), the computer readable storage medium (802) containing instructions executable by the processing circuitry (804), whereby the receiver (120) is configured to: receive, from a transmitter (110) along a first path (130), at least one second post-measurement quantum system; obtain, a first information based on at least one second entangled quantum sub-system of at least one entangled quantum system, the first information indicating a first evolvement of at least one initial entangled quantum system of the at least one entangled quantum system; obtain a second information using the at least one second postmeasurement quantum system, the second information indicating an evolvement of the at least one second post-measurement quantum system.31 .The receiver (120) according to claim 30, configured to perform the method according to any of claims 15 to 22.

32. A computer program (701 , 801 ) comprising instructions which, when executed on: processing circuitry (704) of a transmitter (110), cause the processing circuitry (704) of the transmitter (110) to carry out the method according to any one of claims 1 to 12; and / orprocessing circuitry (804) of a receiver (120), cause the processing circuitry (804) of the receiver (120) to carry out the method according to any one of claims 13 to 22.

33. A tangible, non-volatile computer readable medium (702, 802) comprising instructions that, when executed on processing circuitry (704) of a transmitter (110), cause the processing circuitry (704) of the transmitter (110) to carry out the method according to any one of claims 1 to 12; and / or processing circuitry (804) of a receiver (120), cause the processing circuitry (804) of the receiver (120) to carry out the method according to any one of claims 13 to 22.

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