Methods and apparatuses for time synchronization in communication of quantum information

Abstract

Methods and apparatus for determining correspondence between a first series of optical pulses sent by a first unit and optical pulses received at a second unit involve attempting Bell state measurements (BSMs) at the second unit between the optical pulses from the first unit and optical pulses of a second series of optical pulses. The first series of optical pulses encode information. Results of the BSMs that correspond to one-click events are recorded. An error rate is determined for each of plural trial index alignments between the first series of optical pulses and the second series of optical pulses. A correct index alignment can be determined by selecting one of the trial index alignments for which the error rate is minimized and / or is below a threshold. The methods and apparatus have example application in quantum key distribution.

Description

METHODS AND APPARATUSES FOR TIME SYNCHRONIZATION IN COMMUNICATION OF QUANTUM INFORMATIONField

[0001] The present technology relates to the communication of quantum information. The present technology has particular application to maintaining time synchronization between parties exchanging quantum information by way of lossy optical communication paths. The present technology has example application for quantum key distribution.Background

[0002] Quantum states of quantum systems may be used to store information. A quantum state of a given quantum system can be described by a linear combination of “basis states” that belong to a particular basis (a basis is a set of basis states). It is possible to define many (even an infinite number) of different bases for a quantum system any of which may be used to describe the quantum state of the quantum system.

[0003] For example, one basis that may be used to describe the quantum state of a particular quantum system may be made up of the set of basis states {| >1 > , |i 2 >}. A quantum state of that quantum system may be described by cr|i l > + (3 ip2 >, where a and p are complex valued coefficients. A different basis that may be used to describe the same quantum state of the same quantum system may be made up of the set of basis states {|<pl > , |<p2 >}. Therefore, the same quantum state of the quantum system may also be described by 5|<pl > + y|<p2 > where (5, y) (a, ).

[0004] One may encode information in the quantum state of a system by causing the quantum system to have a quantum state that corresponds to specific values of the coefficients associated with the basis states in a particular basis. To take a simple example the quantum state corresponding to a=1 and p=0 in the> , |i 2 >} basis may be chosen to represent a binary value of 1 or “TRUE” and the quantum state corresponding to a=0 and p=1 in the {| >1 > , |i 2 >} basis may be chosen to represent a binary value of 0 or “FALSE”. Information stored in a quantum system using a particular basis may be recovered by making measurements of the quantum system in that basis. Depending on the basis, the measurement may yield one or more classical values. For some encodings the measurement yields one or more binary values.

[0005] Notably, encoding the same information in the quantum state of the quantum system using different bases results in the quantum system being in different quantum states. For a suitable choice of bases, the encoded information can be reliably recovered only by measuring the quantum system in the same basis that was used to encode the information in the quantum state of the quantum system.

[0006] Quantum information has properties that make quantum information well suited for certain applications. One property is that it is impossible to create a perfect copy of an unknown quantum state (by the “no cloning theorem”) and also that a single unit of quantum information (a “qubit”) has more degrees of freedom than a single unit of digital information (a “bit”) which is limited to having one of the values 0 and 1.

[0007] Individual photons travelling in communication paths may be used to transmit quantum information over distances.

[0008] One problem with transmitting quantum information using photons is that there is a risk that any photon that is emitted into an optical path may be lost before the photon is received. Some optical paths are so lossy that only a small proportion of photons that are emitted into one end of the optical path reach the other end of the optical path.

[0009] There are a wide variety of applications in which it is desirable to transmit quantum information between parties. An example of these applications is quantum key distribution (“QKD”) which allows the parties to share a key that may, for example be used for encryption and decryption of data. QKD exchanges quantum information between the parties. The parties can build a key by making measurements of the quantum information. QKD algorithms may be constructed so that it is impossible for an eavesdropper to learn the quantum key that is shared by the parties.

[0010] In one example of QKD, which is described in Panayi, C., Rzavi, M., Ma, X., & Liitkenhaus, N. (2014). Memory-assisted measurement-device-independent quantum key distribution. New Journal of Physics, each of two parties, “Alice” and “Bob” select a classical bit value and a basis and then encode the classical bit value using the basis as quantum information in a pulse of a train of optical pulses (qubits). Each of Alice and Bob and send a train of optical pulses which encode bit values through a lossy channel, to a central processor, “Charlie”. Charlie receives those of the pulses that are not lost in the lossy channels and stores the quantum information encoded therein in respective quantum memories (QM) using a quantum teleportation (QT)protocol. An example quantum teleportation protocol is described in: Bennet, C. H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., & Wootters, W. K. (1993).Teleporting an unknown quantum state via dual classical and Einstein-Podolsky- Rosen channels. Phys. Rev. Lett.

[0011] For some QT protocols, the storage (loading) process is probabilistic (i.e. even in the absence of photon losses the quantum information is successfully stored in the respective quantum memory with some probability that is less than 1 - e.g. 50%).

[0012] A QKD protocol may use a QT protocol that is heralded. A heralded QT protocol generates a signal that indicates when the quantum information encoded in a pulse has been successfully stored (loaded).

[0013] Once quantum information from Alice and Bob has been successfully loaded into respective ones of Charlie’s quantum memories, Charlie may perform a Bell State Measurement (BSM) on the respective quantum memories. The BSM may also be probabilistic. If the BSM is successful, Charlie sends the BSM results to Alice and Bob. Alice can use the BSM results together with knowledge of the quantum information that Alice encoded in the pulse corresponding to the BSM (i.e. the pulse from Alice that was stored by Charlie and was subjected to the BSM), to obtain information about the quantum information that Bob encoded in the other pulse corresponding to the BSM. Similarly, Bob can use the BSM results together with knowledge of the quantum information that Bob encoded in the pulse corresponding to the BSM, to obtain information about the quantum information Alice encoded in the pulse corresponding to the BSM. Using the information about the quantum information that the other encoded in the corresponding pulse, each of Alice and Bob can obtain a shared raw key bit.

[0014] The above procedure is repeated until Alice and Bob each have enough raw key bits to create a shared secure key that is long enough for the desired cryptographic application.

[0015] The QKD protocol described requires Alice and Bob to know, for each of the BSMs performed by Charlie on stored quantum information from Alice and Bob, which optical pulse that they sent was the source of the stored quantum information used in the BSM. That is, the QKD protocol requires a precise mapping of pulses sent by Alice and pulses sent by Bob to quantum information successfully loaded into a quantum memory by Charlie. Providing such a mapping can be difficult, especially when losses are high and / or the rate at which the optical pulses are sent is high.

[0016] The inventors have identified a need for new ways to track correspondence of quantum information to optical pulses that carry the quantum information.Summary

[0017] The present technology has a number of aspects. These include, without limitation: methods and apparatuses for index synchronization in communication and storage of quantum information; and methods and apparatuses for QKD.

[0018] One aspect of the invention provides methods for determining correspondence between optical pulses sent by a first unit and optical pulses received from the first unit at a second unit. The first unit emits a first series of first unit optical pulses into an optical path that is arranged to deliver the first unit optical pulses to the second unit. Each of the first unit optical pulses encodes information in a photon state of the first unit optical pulse. The method comprises, at the second unit, attempting to perform Bell state measurements (BSMs) between the first unit optical pulses and optical pulses of a second series of optical pulses. Results of those of the attempted BSMs between one of the first unit optical pulses and one of the optical pulses of the second series of optical pulses which correspond to one-click events are recorded. An error rate is determined for each of plural trial index alignments between the first series of optical pulses and the second series of optical pulses. One of the trial index alignments which minimizes the error rate and / or corresponds to an error rate below a threshold, is selected as an index alignment which represents the correspondence between the first unit optical pulses sent by the first unit and the first unit optical pulses of the attempted BSMs.

[0019] The first and second units may be in different clock domains. The optical pulses sent by the first unit may be separated by times that are too short for the optical pulses to be unambiguously identified by their arrival times at the second unit.

[0020] In some embodiments, the optical path is lossy and a success rate for transmission of the first unit optical pulses to the second unit is 20% or less.

[0021] In some embodiments, the method comprises transmitting the recorded results of those of the attempted BSMs which correspond to one-click events to the first unit and performing finding the error rate for each of the trial alignments at the first unit.

[0022] In some embodiments, the information encoded in the photon states of the first unit optical pulses is bit values.

[0023] In some embodiments, for each of the first unit optical pulses the bit value is represented in a corresponding first unit basis selected from a plurality of bases andwherein the attempted BSMs are each performed in a corresponding second unit basis included in the plurality of bases and the method comprises, in determining the error rates for the trial index alignments, ignoring the results of those of the attempted BSMs which correspond to one-click events for which the corresponding first unit basis does not match the corresponding second unit basis.

[0024] In some embodiments, the second unit basis is the same for all of the attempted BSMs.

[0025] In some embodiments, the second unit basis is selected from the plurality of bases and different ones of the attempted BSMs are performed in different ones of the plurality of bases.

[0026] In some embodiments, the method comprises randomly or pseudo-randomly selecting the bit value for each of the first unit optical pulses.

[0027] In some embodiments, the method comprises, at the second unit, determining a time offset relative to arrival times of the first unit optical pulses at the second unit such that the optical pulses of the second series of optical pulses and the first unit optical pulses arrive at a BSA of the second unit substantially simultaneously.

[0028] In some embodiments, the first unit optical pulses are emitted at a rate of at least 1 MHz.

[0029] In some embodiments, the encoding of the information in the first unit optical pulses comprises an encoding selected from the group consisting of: time-bin encoding, polarization encoding, spatial frequency bin encoding, time-frequency mode encoding and combinations thereof.

[0030] In some embodiments, the encoding of the information in the first unit pulses comprises encoding in a higher dimensional photon state having two or more dimensions.

[0031] In some embodiments, each of the first unit optical pulses is constituted by a single photon.

[0032] In some embodiments, at least some of the first unit optical pulses is constituted by a coherent superposition of quantum states.

[0033] In some embodiments, the optical pulses of the second series of optical pulses are emitted from a quantum memory of the second unit.

[0034] In some embodiments, the method comprises: identifying those of the attempted BSMs between the first unit optical pulses and the optical pulses of the second series of optical pulses which correspond to two-click events and for each ofsuch two-click events attempting to load the encoded information of the corresponding first unit optical pulse into the quantum memory of the second unit.

[0035] In some embodiments, the method comprises determining correspondence between optical pulses sent by a third unit and optical pulses received from the third unit at the second unit by: at the second unit, receiving a series of third unit optical pulses from an optical path configured to deliver the third unit optical pulses to the second unit, each of the third unit optical pulses encoding quantum information; at the second unit attempting to perform a BSM between each of the third unit optical pulses sent by the third unit and second unit optical pulses emitted from another quantum memory of the second unit; and recording results of those of the attempted BSMs between the third unit optical pulses and the second unit optical pulses which correspond to one-click events; determining an error rate for each of plural trial index alignments between the third unit optical pulses and the attempted BSMs between the third unit optical pulses and the second unit optical pulses; and selecting one of the trial index alignments between the third unit optical pulses and the attempted BSMs between the third unit optical pulses and the second unit optical pulses which has a minimum error rate and / or for which the error rate is below a threshold as an index alignment which represents the correspondence between the third unit optical pulses sent by the third unit and the attempted BSMs between the third unit optical pulses and the second unit optical pulses. The selected trial index alignments between the third unit optical pulses and the second unit optical pulses and the first unit optical pulses and the second unit optical pulses may be used to generate a correspondence between the third unit optical pulses and the first unit optical pulses.

[0036] In some embodiments, for each of the third unit optical pulses the encoded information comprises a bit value represented in a corresponding third unit basis of the plurality of bases and wherein the attempted BSMs between the third unit optical pulses and the second unit optical pulses are performed in a corresponding second unit basis selected from the plurality of bases and the method comprises identifying those of the attempted BSMs between the third unit optical pulses and the second unit optical pulses which correspond to two-click events for which the corresponding third unit basis matches the corresponding second unit basis using the index alignment which represents the correspondence between the third unit optical pulses sent by the third unit and the attempted BSMs between the third unit optical pulses and the second unit optical pulses.

[0037] In some embodiments, the method comprises: identifying those of the attempted BSMs between the third unit optical pulses and the second unit optical pulses which correspond to two-click events and for each of such two-click events attempting to load the encoded information of the corresponding third unit optical pulse into the corresponding additional quantum memory of the second unit; for each of a plurality of pairs of the quantum memories of the second unit, where each of the pairs includes one of the quantum memories into which the encoded information of one of the first unit optical pulses has been loaded and one of the quantum memories into which the encoded information of one of the third unit optical pulses has been loaded performing a Bell state measurement on the pair of quantum memories.

[0038] In some embodiments, the method comprises making available results of the Bell state measurements on the pairs of quantum memories to at least one of the first unit and the third unit.

[0039] In some embodiments, the optical pulses of the second series of optical pulses are third unit optical pulses generated at a third unit and optically transmitted from the third unit to the second unit.

[0040] In some embodiments, the third unit optical pulses each encode information and the method comprises determining correspondence between the third unit optical pulses sent by the third unit and the first series of optical pulses, respectively received from the third unit and first unit at the second unit by: determining an error rate for each of plural trial index alignments between the third unit optical pulses and the first series of optical pulses; and selecting one of the trial index alignments between the third unit optical pulses and the first series of optical pulses which corresponds to a smallest error rate and / or corresponds to an error rate below a threshold as an index alignment which represents the correspondence between the third unit optical pulses and the first series of optical pulses.

[0041] In some embodiments, some or all of the BSMs are successful BSMs and the method comprises using results of the successful BSMs for quantum key distribution.

[0042] Another aspect of the invention provides methods for determining correspondence between first unit optical pulses originating at a first unit that contain information encoded in photon states of the first unit optical pulses and optical pulses received from the first unit at a second unit. The methods according to this aspect comprise: obtaining data that comprises the information encoded in the first unitoptical pulses; obtaining data comprising measurement results of attempted Bell state measurements (BSMs) performed at the second unit between the first unit optical pulses and optical pulses of a second series of optical pulses, the measurement results corresponding to one-click events; determining an error rate for each of plural trial index alignments between the first series of optical pulses and the attempted BSMs; and selecting one of the trial index alignments which minimizes the error rate and / or corresponds to an error rate below a threshold, as an index alignment which represents the correspondence between the first unit optical pulses sent by the first unit and the first unit optical pulses of the attempted BSMs.

[0043] In some embodiments, the method comprises using measurement results of those of the attempted BSMs that correspond to two-click events for quantum key distribution.

[0044] Another aspect of the invention provides systems operable to determine correspondence between optical pulses sent by a first unit and optical pulses received from the first unit at a second unit. The first unit emits a first series of first unit optical pulses. Each of the first unit optical pulses carry information encoded in a photon state of the first unit optical pulse. The system including the second unit, the second unit comprising: a Bell state analyzer (“BSA”); at least one optical port optically connectible to the BSA; and a control system including a controller. The controller is operative to: monitor results of measurements by the BSA corresponding to attempted Bell state measurements (“BSMs”) between the first unit optical pulses and optical pulses of a second series of optical pulses; record results of those of the attempted BSMs between one of the first unit optical pulses and one of the optical pulses of the second series of optical pulses which correspond to one-click events. The control system is operative to: determining an error rate for each of plural trial index alignments between the first series of optical pulses and the second series of optical pulses; and select one of the trial index alignments which minimizes the error rate and / or corresponds to an error rate below a threshold, as an index alignment which represents the correspondence between the first unit optical pulses sent by the first unit and the first unit optical pulses of the attempted BSMs.

[0045] Another aspect of the invention provides a system for determining correspondence between first unit optical pulses originating at a first unit that contain information encoded in photon states of the first unit optical pulses and optical pulses received from the first unit at a second unit. The system comprises a data processorconfigured to process: data that comprises the information encoded in the first unit optical pulses; with data comprising measurement results of attempted Bell state measurements (BSMs) performed at the second unit between the first unit optical pulses and optical pulses of a second series of optical pulses where the measurement results correspond to one-click events to determine an error rate for each of plural trial index alignments between the first series of optical pulses and the attempted BSMs; and selecting one of the trial index alignments which minimizes the error rate and / or corresponds to an error rate below a threshold, as an index alignment which represents the correspondence between the first unit optical pulses sent by the first unit and the first unit optical pulses of the attempted BSMs.

[0046] Another aspect of the invention provides apparatus having any new and inventive feature, combination of features, or sub-combination of features as described herein.

[0047] Another aspect of the invention provides methods having any new and inventive steps, acts, combination of steps and / or acts or sub-combination of steps and / or acts as described herein.

[0048] Further aspects and example embodiments are illustrated in the accompanying drawings and / or described in the following description.

[0049] It is emphasized that the invention relates to all combinations of the above features, even if these are recited in different claims.Brief Description of the Drawings

[0050] The accompanying drawings illustrate non-limiting example embodiments of the invention.

[0051] Fig. 1 is a flow chart that illustrates an example procedure for loading quantum information into a quantum memory using quantum teleportation.

[0052] Figs. 1A and 1 B are schematic diagrams that illustrate stages in the execution of the procedure of Fig. 1.

[0053] Fig. 2 is a flow chart that illustrates a method according to an example embodiment of the invention.

[0054] Fig. 2A shows example time distributions of photon detections for optical pulses originating from first and second units.

[0055] Fig. 2B shows example timing of optical pulses at first and second inputs of a Bell state analyzer.

[0056] Fig. 2C shows an example of optical pulses at first and second inputs of a Bellstate analyzer where some optical pulses are lost.

[0057] Figs. 2D, 2E, 2F and 2G are schematic drawings illustrating example

[0058] Fig. 3 is a flow chart that illustrates an index alignment method according to an example embodiment of the invention.

[0059] Fig. 3A is a plot of error rate for one-click events as a function of index alignment for simulated data.

[0060] Fig. 4 is a block diagram illustrating an apparatus according to an example embodiment of the invention. Fig. 4A illustrates operation of the apparatus of Fig. 4.

[0061] Fig. 5 is a block diagram illustrating an apparatus according to another example embodiment of the invention.Detailed Description

[0062] Throughout the following description, specific details are set forth in order to provide a more thorough understanding of the invention. However, the invention may be practiced without these particulars. In other instances, well known elements have not been shown or described in detail to avoid unnecessarily obscuring the invention. Accordingly, the specification and drawings are to be regarded in an illustrative, rather than a restrictive sense.

[0063] One aspect of this invention relates to methods and apparatus for making quantum measurements on pairs of photon states. The photon states in each pair correspond to optical pulses that are respectively issued from first and second sources. Such measurements may be used, for example, in quantum teleportation protocols, quantum key distribution protocols, quantum communication protocols, protocols for creating quantum entanglement of distributed quantum systems and other applications. Various applications require that such measurements be made for multiple pairs of photon states. For such applications the first and second sources may each be caused to emit a series (or sequence) of optical pulses at times spaced apart by a set period. Measurements may be made on photon states of multiple pairs of the optical pulses.

[0064] In order to make such measurements on any pair of photon states the photon states must be able to interact at a suitable detector. For such interaction to occur the optical pulses that correspond to the photon states need to be present substantially simultaneously at the detector. This requires coordination of the times at which optical pulses are emitted from the first and second sources. Establishing such coordination may be called “pulse synchronization”.

[0065] Pulse synchronization may be achieved by advancing or retarding optical pulses from one of the first and second sources by a time offset. The time offset is not unique since adding or subtracting to the time offsets the period that separates adjacent optical pulses or a multiple of that period will yield another time offset that will cause optical pulses from the first and second sources to be present at the detector substantially simultaneously.

[0066] In some applications, the photon states of different ones of the optical pulses emitted by the first source and / or the second source differ from one another. For example, different information may be encoded in different ones of the photon states and / or information may be encoded in different ones of the photon states using different bases. For such applications it can be important to know which optical pulse from the first source and which optical pulse from the second source correspond to the photon states of each measurement. Making this determination may be described as “index alignment”. Each optical pulse from the first source may be associated with a corresponding first source index value and each optical pulse from the second source may be associated with a corresponding second source index value. Index alignment may associate each measurement with a pairing of a first source index value and a second source index value.

[0067] Index alignment is required particularly in cases where the first source and the second source are in separate clock domains and the optical paths by which the optical pulses are carried to the detector are lossy (such that some optical pulses that are emitted by the first source and / or some optical pulses emitted by the second source fail to reach the detector).

[0068] The following description discusses example methods and apparatus according to the present invention which includes: example methods and apparatus for loading quantum information into a quantum memory (see e.g. Figs 1 to 3A and accompanying discussion); example methods and apparatus for quantum key distribution which incorporate quantum memories (see e.g. Figs. 4 and 4A and accompanying discussion), and example methods and apparatus for quantum key distribution which do not require quantum memories (see e.g. Fig. 5 and accompanying discussion). Those of skill in the art will understand from these examples that the methods and apparatus described herein may also be extended to other applications.

[0069] Fig. 1 is a flow chart that illustrates an example procedure 10 for loadingquantum information into a quantum memory using quantum teleportation. Figs. 1A and 1 B illustrate states of an example apparatus at steps of procedure 10. The Example apparatus includes a unit 12C into which quantum information originating from another unit 12A is teleported. For some applications the apparatus may include additional units. For example unit 12C may receive quantum information from a unit 12B in addition to unit 12A (see e.g. Fig. 4).

[0070] At block S11 , (see also Fig. 1 A), information is encoded in the quantum state of an optical pulse 11A at a unit 12A. The information may, for example, be encoded in a polarization state, a time bin state, a spatial frequency bin state, time-frequency mode, or the like. In some embodiments information is encoded in a higher dimensional (two or more dimensional) photon state.

[0071] In some embodiments, optical pulse 11 A is made up of a single photon. In some embodiments optical pulse 11A is a weak coherent pulse. Optical pulse 11 A is emitted into an optical path AC by way of which optical pulses can travel from unit 12A to a first input port of a Bell State Analyzer (“BSA”) 16. Optical path MAC and other optical paths described herein may be of any type that can carry optical pulses from a given source to a desired destination. For example, an optical path may be made up of one or more: waveguides (e.g. optical fibres, integrated waveguides, strip waveguides, liquid waveguides etc.) and / or free space optical paths through space, air, water or other light-transmitting medium.

[0072] Encoding the quantum information into the quantum state of optical pulses 11 A may, for example, comprise applying an encoder. The encoder may, for example, comprise selected filter(s) and / or modulators 17-1 which collectively modulate a pulse of light emitted by a light source 17-2 such as a laser. In the example of Fig. 1A, light source 17-2 and filter(s) 17-1 are controlled by a controller 19A to encode the quantum information in optical pulses 11 A. Another example way to encode quantum information into optical pulse 11 A is to place a quantum system of unit 12A into a selected quantum spin state and cause the quantum system to emit optical pulse 11 A as a spin entangled photon.

[0073] At block S12 optical pulse 11 A travels toward BSA 16 of unit 12C.

[0074] At block S13 (see also Fig. 1 B) a unit 12C causes emission of an optical pulse 11C into an optical path 14CC by way of which optical pulses 11C can travel to a second input port of BSA 16. In some embodiments optical pulse 11C consists of a single photon. In some embodiments optical pulse 11C is a weak coherent pulse. Thephotons of optical pulses 11 A and 11 C are ideally indistinguishable except for one or more degree of freedom in which quantum information is encoded. In this example, optical pulse 11C is entangled with a quantum state of a quantum memory 18 of unit 12C. In other example embodiments (see e.g. Fig. 5) optical pulses that are delivered to the second input port of BSA 16 come from another source such as a unit 12B.

[0075] The emission of optical pulse 11C is timed so that optical pulses 11A and 11C will arrive at BSA 16 substantially simultaneously. To achieve this, unit 12C causes optical pulse 11C to be emitted at a time that is before the expected time of arrival of optical pulse 11A at BSA 16 by a time offset. Here, “substantially simultaneously” means that optical pulses 11A and 11C are present simultaneously at BSA 16 such that a measurement such as a Bell state measurement (“BSM”) may be performed on optical pulses 11A and 11C. A Bell state measurement is a projective measurement on two quantum systems (e.g. two photons) into a Bell state or other maximally entangled state. In some embodiments, “substantially simultaneously” is achieved when optical pulses 11 A and 11 C arrive at BSA 16 at times that are 1 ns or less apart.

[0076] Synchronizing the arrival time of the pulses at a BSA or other detector (pulse synchronization) to within 1 ns or less may be achieved in any of several ways. For example, if optical pulses 11 A and 11C include empty pulses (i.e. , pulses containing zero photons), a time histogram of the arrival time of non-empty pulses of 11 A and 11C associated with respective empty pulses 11C and 11A may be generated and used in computing an arrival time offset between the optical pulses 11A and 11C.

[0077] Another approach determines a frequency offset between optical pulses 11 A and 11C. The frequency offset may be computed by generating a linear fit for multiple arrival time offsets. The frequency offset may be provided to units 12A and / or 12C.

[0078] In some embodiments, only one of optical pulses 11A and optical pulses 11C includes empty pulses. For example, consider a case where optical pulses 11A includes empty pulses and optical pulses 11C does not include empty pulses. In this case one may generate: a first time histogram of arrival times of optical pulses 11 C that correspond to empty pulses 11A; a second time histogram plot of the arrival times of optical pulses 11C that correspond to non-empty pulses 11A. A third time histogram of arrival times of non-empty optical pulses 11 A may then be generated by taking a weighted difference of the first and second time histograms, such that the first time histogram and the third time histogram can be used in computing the arrival time offset.

[0079] The arrival time offset or frequency offset obtained, for example, by one of the approaches outlined above may be used in computing an absolute time offset modulo the period between sequential ones of optical pulses 11 A (and 11C). The absolute time offset may be fed back to units 12A and / or 12C. Units 12A and / or 12C may use the absolute time offset to adjust their timing for delivering pulses 11A and 11C.

[0080] Returning now to Fig 1 B, at block S14, a BSM is performed on optical pulses 11 A and 11 C. The BSM is probabilistic in that the BSM has a probability of success that is non-zero and less than 100% and a probability of failure that is non-zero and less than 100%. In some embodiments, not including failures due to the loss of optical pulses, the probability of success is 50%.

[0081] At block S16, if the BSM at block S14 succeeded, a result of the BSM is used to generate a unitary transformation (i.e. , a unitary transformation is generated based on the result of the BSM).

[0082] At block S17 the unitary transformation from block S16 is applied to quantum memory 18, for example, by a controller of unit 12C. The result of applying the unitary transformation to quantum memory 18 is that the quantum information stored in memory 18 is the same as the quantum information that was encoded in optical pulse 11A. Process 10 does not provide unit 12C with knowledge of the information that was encoded in optical pulse 11 A or the quantum state stored in quantum memory 18.

[0083] To practice process 10, it is necessary to know when optical pulse 11A is expected to arrive at BSA 16 and the time offset to be applied in block S13.

[0084] Where optical pulse 11 A is one of a series (or equivalently a sequence) of optical pulses 11A that are delivered in sequence an index value may be assigned to each optical pulse in the series of optical pulses by unit 11A. Unit 11C may also assign index values to optical pulses 11 C. The same index values assigned to an optical pulse 11C may also be associated with an attempted Bell State Measurement (BSM) involving the optical pulse 11 C, an optical pulse 11 A received at unit 12C that arrives at BSA 16 substantially simultaneously with the optical pulse 11 C as well as quantum information that has been loaded into quantum memory 18 using the particular optical pulse 11 C.

[0085] It is typically necessary or desirable to know the relationship of the index value assigned to an optical pulse 11 A by unit 12A and the index value assigned to a corresponding optical pulse 11C by unit 12C (where an optical pulse 11 Ccorresponds to an optical pulse 11A when the optical pulse 11 C is substantially simultaneously present at BSA 16 with the optical pulse 11 A). Knowledge of this relationship is necessary to keep track of what quantum information has been loaded into quantum memory 18 from an optical pulse 11 A received at unit 12C.

[0086] In this example, unit 12A assigns index values to the optical pulses 11A that are sent toward unit 12C and unit 12C assigns index values to optical pulses 11C that are delivered to BSA 16. In this example, index alignment involves determining a correspondence between the index values assigned to optical pulses 11 A by unit 12A and the index values assigned to corresponding optical pulses 11C by unit 12C (the index value for an optical pulse 11 C can also be associated with a corresponding received optical pulse 11 A, a corresponding attempted BSMs involving the optical pulse 11C, and, if the quantum teleportation succeeds, an corresponding item of quantum information stored in quantum memory 18). In other words, index alignment provides information about the correspondence between optical pulses 11 A and optical pulses 11C, and items of quantum information stored in quantum memory 18.

[0087] The index alignment may not be initially known, for example, where optical path AC is lossy, unit 12C cannot assume that the first optical pulse 11A received in a particular series is the first optical pulse in the series. Maybe some number of optical pulses at the beginning of the series were lost. Furthermore, especially where optical pulses 11A are sent in rapid succession, clocks of units 11A and 11C may not be synchronized sufficiently accurately to be able to determine the index alignment based on the times at which optical pulses 11 A are transmitted and received. In some cases performing index alignment based on timing would require that units 11 A and 11C have clocks that are synchronized to within less than one nanosecond to allow precise mapping of sent pulses 11A to successful loadings into quantum memory 18. Maintaining such accurate clock synchronization is typically impractical and / or not cost effective. It is generally more practical for units 11 A and 11C to have clocks that are synchronized in frequency but do not share a precise absolute time. For example, units 11 A and 11 C may agree on absolute time on a millisecond scale.

[0088] Fig. 2 is a flow chart that illustrates a method 20 according to an example embodiment of the invention. Method 20 achieves clock frequency synchronization between first unit 12A and second unit 12C sufficient to load quantum information encoded in optical pulses 11A originating at first unit 12A into one or more quantum memories 18 of second unit 12C by quantum teleportation. Method 20 also performsindex alignment.

[0089] At block S21 frequencies of clocks 15A and 15C of units 12A and 12C respectively are synchronized. The synchronization may involve adjusting frequencies of clock 15A and / or 15B and / or determining values for one or more correction factors. Synchronization of clocks 15A and 15B may be performed, for example, using a distributed reference signal.

[0090] In an example embodiment, block S21 comprises unit 12A controlling a laser or other light source to emit a sequence of optical pulses at set times. For example, the optical pulses may be sent at equally spaced apart times. Unit 12C monitors the timing of the optical pulses (e.g. by noting the time of arrival of each of the optical pulses and / or by measuring a time for receiving a number of the optical pulses). Unit 12C then sets clock 15C based on the results of the measurements. In some embodiments unit 12C uses BSM 16 as an optical pulse detector.

[0091] Clock 15A of unit 12A controls the timing of emission of optical pulses 11A. For clear visualization of the operation of method 20 it is convenient to consider the case where optical pulses are emitted from unit 12A at equally spaced times that coincide with “ticks” of clock 15A and that clocks 15A and 15C are adjusted to tick at the same rate. In some embodiments, optical pulses 11A are emitted at a rate that is in the range of about 50 MHz to 5 GHz (i.e. the pulse-to-pulse period is in the range of about 0.2 ns to about 20 ns).

[0092] Clock 15C of unit 12C controls the timing of emission of optical pulses 11C. When the frequencies of clocks 15A and 15C are synchronized (i.e. clocks 15A and 15C agree on the length of the pulse-to-pulse period between the starts of subsequent optical pulses), if unit 12A always emits optical pulses at a particular phase of the cycle of clock 15A (in this example, at a time that coincides with each tick of clock 15A) then the times at which optical pulses 11A arrive at BSA 16 will correspond to a particular phase of the cycle of clock 15C. The phases of clocks 15A and 15C do not need to be aligned.

[0093] Block S22 determines the times at which unit 12C should cause optical pulses 11C to be emitted such that an optical pulse 11 C will arrive at BSA 16 substantially simultaneously with an optical pulse 11A from unit 12A. In this example, clock 15C has been adjusted to tick at the same rate as clock 15A and so the times at which optical pulses 11C should be emitted can be expressed as a time offset relative to the ticks of clock 15C.

[0094] The time offset may be determined, for example by, causing optical pulses 11C to be emitted at some known time relative to ticks of clock 15C (e.g. emitting optical pulses 11C at times that coincide with the ticks of clock 15C) and determining the time offset between detection of optical pulses 11C and optical pulses 11A at BSA 16. Without loss of generality, as long as optical pulses 11A are equally spaced apart, the time offset can be expressed as times within a range that has a length equal to the spacing between pulses 11 A (in this example, one period of clock 15C). In other words, the time offset may be determined modulo the period of clock 15C.

[0095] A complication in measuring the time offset is that optical pulses 11A and 11C have non-zero pulse widths and so the times of detection of photons corresponding to pulses 11A or 11C are distributed according to a distribution such as a Gaussian distribution that has a width corresponding to the pulse width. The widths of optical pulses 11A and / or 11C (which may be expressed as full width at half maximum) may, for example, be on the order of 0.1 ns to 10 ns. This complication may be overcome by collecting measurements of enough photons from optical pulses 11 A and 11 C (e.g. several hundred photon detections) to determine centers of the distributions of detections corresponding to pulses 11A and 11 C with a desired degree of precision and to set the time offset based on the centers of the distributions. In cases where the time for an optical pulse 11C to be detected after it is emitted is either negligible or known and the characteristics of pulses 11C are known well enough that the centers of pulses 11C can be made to coincide with a selected time (e.g. the ticks of clock 15C) it is optional to detect pulses 11 C at BSA 16 since the time at which optical pulses 11C would be detected is known.

[0096] Fig. 2A shows an example time distribution 21 C of photon detections corresponding to optical pulses 11C and an example time distribution 21 A of photon detections corresponding to optical pulses 11A. Time zero corresponds to ticks of clock 15C. A time offset 22 between distributions 21 C and 21 A is determined by computing the time difference between centers and / or peaks of distributions 21 C and 21A. In this example the time offset is 44.6 ns.

[0097] Using the determined time offset unit 12C can cause optical pulses 11C to be emitted at time such that optical pulses 11C and 11A are present substantially simultaneously at BSA 16. This may be done by causing pulses 11 C to be delayed by the time offset relative to ticks of clock 15C. Thus, quantum information encoded in optical pulses 11A may be loaded into quantum memories 18 of unit 12C, for exampleusing a quantum teleportation procedure such as procedure 10 of Fig. 1.

[0098] The foregoing discussion uses the metaphor of “ticks” to represent the time measured by clocks 15A and 15C. The oscillators or other time references of clocks 15A and 15C may operate at any suitable frequencies. Clock 15A may have any construction that enables timekeeping suitable for causing emission of optical pulses 11A at desired times. Clock 15C may have any construction that enables timekeeping suitable for causing emission of optical pulses 11C at desired times.

[0099] There remains the index alignment problem of matching specific quantum information encoded by unit 12A into a particular optical pulse 11A to quantum information that has been loaded into a specific quantum memory 18 of unit 12C. This problem is contributed to by factors such as the time required for optical pulses 11 A to propagate from unit 12A to BSA 16 may not be known at all or may be known only imprecisely, even if clocks 15A and 15C are both frequency stable, the relationship between the absolute time as measured by clock 15A and the absolute time as measured by clock 15C may include significant uncertainty, and optical pulses 11A may be emitted at a high rate. A complication is that the paths taken by optical pulses 11 A and 11 C are generally lossy, meaning that some of (and in some cases most of) optical pulses 11A and / or 11C may fail to be detected at BSA 16. In the case where unit 12A sends a series of optical pulses 11A toward BSA 16, unit 11 C cannot be sure that the first optical pulse 11A detected at BSA 16 is the first optical pulse 11A in the series because it is possible that a string of one or more optical pulses 11 A at the beginning of the series were not received as a result of photon losses.

[0100] Another factor that can affect index alignment is that the times that it takes for optical pulses 11A and 11C to reach BSA 16 may vary with time. For example, the effective path lengths taken by optical pulses 11A and / or 11 C may vary with temperature (e.g. as a result of changes in index of refraction and / or length of optical waveguides such as optical fibers), or one or both of units 12A and 12C may be moving relative to the other one of units 12A and 12C (e.g. a unit 12A or 12C may be carried on a moving platform such as a satellite, aircraft, road vehicle, ship etc. such that optical pulses 12A must travel by a variable distance through free space to reach BSA 16.

[0101] At block S23, units 12A and 12C agree on a time at which unit 12A will commence sending a series of optical pulses 11A toward BSA 16. Because clocks 15A and 15C do not share a common absolute time, from the point of view of unit12C, there is a time window within which the first pulse of the series of pulses 11A from unit 12A could arrive. That time window may have a length that is longer than the time that separates sequential ones of the series of optical pulses 11 A.

[0102] At block S24 the optical pulse sequence is delivered. Unit 12A commences generating and sending toward BSA 16 the sequence of optical pulses 11A starting at the time agreed to in block S23 (according to clock 15A).

[0103] Each optical pulse 11 A includes encoded information. The information is encoded in one of a plurality of bases. In this example, for any measurement, BSA 16 is configured to be aligned with one of the plurality of bases. With BSA 16 aligned with a particular one of the plurality of bases the BSA 16 may resolve two of the four Bell states, thus providing a “more-complete” Bell state measurement as compared to cases in which a BSA is not aligned to a particular basis and can resolve only one of the Bell states. In some embodiments BSA 16 is selectively configurable to be aligned with any one of the plurality of bases. In some embodiments the alignment of BSA 16 with a particular one of the plurality of bases is fixed.

[0104] Though the BSA 16 is designed to make projective measurements onto two- photon Bell states, BSA 16 can also be used to make measurements on single photon or single-pulse states, where only one detector clicks (“single-click measurements”). Where information is encoded in an optical pulse using a selected basis and the BSA is aligned with the selected basis then, in the case where the information is encoded by setting the photon state to be one of the basis states of the selected basis, then a single-click measurement by the BSA 16 will be deterministic. On the other hand, if the BSA is not aligned with the selected basis then a measurement by BSA 16 will not be deterministic. In some embodiments, two bases are selected such that measurements by BSA 16 will be deterministic when BSA 16 is aligned with the basis in which information is encoded and measurements by BSA 16 will be random when BSA 16 is aligned with the other basis.

[0105] As an example of a basis, a photon may have basis states |pl > and |p2 > (which may, for example be different orthogonal polarization states or different time bin states, different spatial frequency states etc.). Information may be encoded in a photon system in a first basis by causing the photon to have a quantum state given by the superposition: <z|pl > +(3\p2 > where a and p are, in general, complex valued coefficients with |<z2| + | / ?2| = 1. One way to encode a classical bit value in this basis is to set a=1 and p=0 to represent a classical bit value of “1” and to set a=0 and p=1to represent a classical bit value of “0”. In the alternative, the same quantum information may be encoded in the photon in a second basis by causing the photon to have the state: -=(|pl > +|p2 >) + -7= (|pl > - |p2 >). A classical bit value may be v2 y2 encoded in this basis as described above. If a classical bit value is encoded in quantum information using the second of these bases and then a measurement is performed using the first of these bases then the result of the measurement will be random. The same applies when the classical bit value is encoded using the first basis and the measurement is made in the second basis.

[0106] As is known in the art, the construction of BSA 16 can depend on which basis or bases BSA 16 is designed to measure in. Fig. 2D shows an example BSA 16 which has first and second input ports 27A-1 and 27A-2 that connect to inputs of an interference device 27B. Interference device 27B allows interference between photon states received at input ports 27A-1 and 27A-2. Interference device 27B may for example comprise a beamsplitter. Outputs of interference device 27B are connected to a measurement system 27C which is aligned or alignable to make measurements in a particular basis.

[0107] Fig. 2E shows an example BSA 16-1 in which measurement system 27C comprises first and second single photon detectors 28A and 28B. BSA 16-1 may, for example, be used to measure whether a photon state is an early or late time bin by direct measurement of the time at which a photon state is detected by a click at one of single photon detectors 28A and 28B.

[0108] Fig. 2F shows an example BSA 16-2 that is similar to BSA 16-1 except that it includes interferometers 27D. A BSA having a structure like that of BSA 16-2 may be used to measure whether a photon state corresponds to the state: |+) = -^=( early > +\late >) or the state I state in whicha photon is in an early time bin and \late > is a state in which the photon is in a late time bin.

[0109] Fig. 2G shows an example BSA 16-3 wherein measurement system 27C comprises a pair of polarizing beam splitters 27D-1 and 27D-2 and single photon detectors 28A-1 , 28A-2, 28B-1 and 28B-2. A BSA having a structure like that of BSA 16-3 may be used to measure whether a photon state corresponds to a first polarization state that polarizing beam splitter 27D-1 or 27D-2 directs for photon detection at photon detector 28A-1 or 28B-1 or a second polarization state thatpolarizing beam splitter 27D-1 or 27D-2 directs for photon detection at photon detector 28A-2 or 28B-2.

[0110] Designs for measurement systems operable to measure photon states in a wide variety of different bases are known to those of skill in the art. The BSAs illustrated in Figs. 2D to 2G are examples only.

[0111] Blocks S25A, S25C, S26 and S27 are performed for each optical pulse 11 A. Block S25A generates the optical pulse 11 A with encoded quantum information.

[0112] Unit 12A maintains a record of the encoded quantum information and the basis used to encode the quantum information in each optical pulse 11 A. The quantum information may, for example, encode a classical bit value (“1” or “0”). For some applications, unit 12A may randomly select the classical bit value to be encoded in the quantum information of each optical pulse 11 A.

[0113] At block S25C, unit 12C causes a quantum memory to emit an optical pulse 11C at a time such that the optical pulse 11C should arrive at a BSA 16 in time to be present in BSA 16 substantially simultaneously with a corresponding optical pulse 11A. The optical pulse 11C may be emitted toward BSA 16 at a time corresponding to the time offset discussed elsewhere herein.

[0114] In some embodiments different optical pulses 11C are emitted from different quantum memories of a set comprising a plurality of quantum memories 18. The set of quantum memories 18 may be controlled to emit a sequence of optical pulses 11 C.

[0115] In some embodiments, block S24 causes the first optical pulse 11C of the series to be emitted at a time that is early enough that the first optical pulse 11C of the series is expected to arrive at BSA 16 one, two or more ticks of clock 15C prior to the expected arrival at BSA 16 of the first optical pulse 11 A in the series of optical pulses commenced in block S24.

[0116] Block S26 attempts to perform BSMs on corresponding optical pulses 11A and 11C.

[0117] Block S27 stores (e.g., records) results of measurements made in block S26.

[0118] After a sequence of optical pulses 11A has been generated and sent toward BSA 16 block S27 will have acquired and recorded a series of measurement results from BSA 16.

[0119] Assuming the photons of optical pulses 11A and 11C are indistinguishable except for their encoded degree of freedom, and that BSA 16 is an ideal optical BSA, there are three possible outcomes of measurement by BSA 16 as follows:1 . A photon corresponding to optical pulse 11 A and a photon corresponding to optical pulse 11C each arrive at BSA 16 and are each detected at BSA 16 (a “two- click event”);2. A photon corresponding to one of optical pulses 11A and 11C is lost in transit and a photon corresponding to the other one of optical pulses 11A and 11C is detected at BSA 16, or, a photon corresponding to optical pulse 11 A and a photon corresponding to optical pulse 11C each arrive at BSA 16 and trigger the same detector (a “one-click event”);3. Both photons are lost in transit and no photon is detected at BSA 16 (a “zeroclick event”).Successful heralded loading of quantum information from an optical pulse 11 A into a quantum memory 18 according to procedure 10 requires a two-click event. As is known in the art, in the case of a one-click event or a zero click event the quantum state that was intended to be teleported into quantum memory 18 is lost.

[0120] In many practical applications of the present technology a significant number (on some cases many or most) of the BSMs attempted in block S26 will correspond to one-click events. Therefore, the measurement results recorded in block S27 will typically include measurement results that correspond to one-click events. In many practical applications of the present technology most of the BSMs attempted in block526 will correspond to one-click or zero click events due to photon losses.

[0121] Block S27 records information about successful detection events (two-click events) and failed detection events (one-click events). For the two-click events block527 records the detection of two photons and the results of measurements on each of the photons in a basis (“BSA measurement basis”). In some embodiments the BSA measurement basis is fixed. In some other embodiments the BSA measurement basis is selected from a plurality of bases. At least in those embodiments where the BSA measurement basis is not fixed unit 12C records the measurement basis used for each measurement.

[0122] For one-click events, the attempted BSMs of block S26 result in measurements of the photon state which caused the one-click events in a measurement basis. The measurements may, for example comprise: measuring whether the detection (“click”) occurred at a time corresponding to an early or late time bin and / or determining which of a plurality of single photon detectors was triggered in the one-click event.

[0123] Fig 2B shows an example timing of optical pulses 11A and 11 C at inputs of BSA 16. Optical pulses 11A are individually identified as 11A-0, 11 A-1 , 11A-2 ... etc. Optical pulses 11 C are individually identified as 11 C-0, 11 C-1 , 11 C-2 ... etc. Due to the fact that clocks 15A and 15C do not precisely agree on an absolute time, there is uncertainty at unit 12C regarding when (according to clock 15C) to expect optical pulse 11 A-0. This uncertainty is represented by window 33. Also shown in Fig. 2B is an expected arrival time 34 for optical pulse 11 A-0. In this example, optical pulse 11C-0 arrives at BSA 16 two cycles of clock 15C prior to expected arrival time 34. This allows for five possible index alignments (i.e. alignment of optical pulse 11 A-0 with any one of optical pulses 11C-0 to 11C-4) to accommodate absolute time uncertainty of up to + / - two cycles of clock 11C. Some embodiments can accommodate absolute time uncertainty of up to a larger number of cycles of clock 15C.

[0124] In the example of Fig. 2B, optical pulse 11 C-0 arrives at BSA 16 four cycles of clock 15C prior to optical pulse 11A-0.

[0125] As discussed elsewhere herein, individual optical pulses 11A and / or 11C may fail to be detected at BSA 16, for example due to being lost in transit. Fig 2C illustrates this possibility. In Fig. 2C, optical pulses that are lost before they are detected (e.g. optical pulses that fail to arrive at unit 12C) are shown in dotted lines, optical pulses that are detected are shown in solid lines, optical pulses that correspond to one-click events 26 are filled with parallel hatching and optical pulses that correspond to two-click events 24 are filled with cross hatching. Fig. 2B shows a total of ten one-click events and four two-click events.

[0126] Because any optical pulsel 1A or 11C could be lost, the first optical pulse 11 A detected at unit 12C cannot simply be equated to optical pulse 11A-0. Maybe one or several optical pulses at the beginning of the series of optical pulses sent by unit 12A are lost so that the first optical pulse 11A that is detected at BSA 16 could be optical pulse 11 A-1 , or 11 A-2 etc. In the Fig. 2C example, optical pulses 11 A-0 and 11 A-1 are both lost and not detected. Furthermore, as is known in the art, BSA 16 typically cannot determine whether a detected photon came from unit 12C or unit 12A.

[0127] Block S28 identifies one-click events 26 and two-click events 24.

[0128] Block S29 performs an index alignment method using results of measurements corresponding to one-click events stored by block S27.

[0129] Block S30A uses the results of the index alignment of block 30A to matchindices for the two-click events. Block S30B uses the two-click events (e.g. for quantum key distribution or other secure communication of information).

[0130] In some embodiments block S27 transmits or otherwise makes available the results of the measurements (at least for the one-click events) to unit 12A and block S29 is performed at unit 12A.

[0131] Fig. 3 is a flow chart that illustrates an index alignment method 30 which allows two-click events (and any resulting stored quantum information) to be associated to the quantum information encoded in a specific optical pulse 11 A. Block S29 of Fig. 2 may, for example, comprise performing index alignment method 30.

[0132] At block S31 , at least some of the information recorded at block S27 is communicated to unit 12A. For example, block S31 may comprise unit 12C sending results of measurements performed by BSA 16 corresponding to one-click events to the relevant one of units 12A (and 12B if present) together with information identifying indices assigned by unit 12C corresponding to those one-click events and, where applicable, a measurement basis used by a BSA 16 of unit 12C.

[0133] Loop S32 tests different index alignments of optical pulses 11 A to optical pulses 11C. In each iteration of loop S32 a trial index alignment is tested. Block S32A selects a trial alignment to test. In the current example, for each iteration of loop S32 block S32A may select one of the five possible trial alignments described with reference to Fig. 2B to test. Other embodiments may test a different number of trial alignments.

[0134] Block S32B processes the one-click events for the current trial alignment to identify those of the one-click events for which the BSA measurement basis matched the basis used at unit 12A to encode the quantum information in the optical pulse 12A corresponding to the one-click event according to the current trial alignment. In some embodiments, block S32B ignores those one-click events for which the BSA measurement basis does not match the basis used at unit 12A to encode the quantum information in the optical pulse 12A corresponding to the one-click event according to the current trial alignment.

[0135] For each of the one-click events where the BSA measurement basis and encoding basis match, block S32C compares the result of the measurement by BSA 16 to the quantum information encoded in the optical pulse 11A by unit 12A. The comparison may be done, for example, by deducing from the measurement result a classical bit value encoded in the quantum state of the optical pulse 11A that ispresumed to match the measurement according to the current trial index alignment and comparing the deduced classical bit value to the bit value that was encoded in that optical pulse 11 A. In the case where the measurement basis and encoding basis match, the encoded bit value can be accurately deduced from the measurement result.

[0136] If the indexes for optical pulses 11A and optical pulses 11C are not correctly aligned in the current trial alignment then the results of the comparisons performed by block 32C are expected to be random (average 50% error rate) assuming that unit 12A selects classical bit values to encode in the quantum information at random. By contrast, if the indexes for optical pulses 11A and optical pulses 11C are correctly aligned in the current trial alignment then the results of the comparisons performed by block S32C is expected to show a correlation between the measurement result from BSA 16 and the quantum information encoded in the corresponding pulse 11A. In a perfect system, where optical pulses 11A and optical pulses 11 C are equally likely to be lost the average error rate is expected to be 25%. If optical pulses 11A are more likely to be lost than optical pulses 11 C then the average error rate may be higher than 25% but less than 50%.

[0137] Block S32D determines statistics for the results of the comparisons performed by block S32C. In some embodiments the statistics comprise an average error rate over all one-click events for a current trial alignment.

[0138] Block 32 E analyzes the statistics of block 32 D to determine the correct index alignment. The correct index alignment represents the correspondence between optical pulses 11A and optical pulses 11C. In some embodiments block 32E compares the statistics for different trial alignments to a threshold. The threshold is chosen to allow identification of one of the trial index alignments that corresponds to the correct index alignment. Comparison of the statistics to the threshold indicates whether a trial index alignment is correct or not correct. For example, where the statistics comprises an average error rate, the average error rate may be compared to a threshold that is between an average error rate expected for incorrect index alignment and an average error rate expected for correct index alignment. In the present example, the threshold may, for example, be set to an error rate that is below 50% and above 25% (e.g. 30% or 40%). The average error rate may be increased in the case where BSA 16 is not accurately aligned with a basis in which information is encoded in photon states. If this misalignment is not too severe then method 30 cansucceed in determining the correct index alignment as long as a suitable threshold is used.

[0139] In addition to or as an alternative to comparing statistics for trial index alignments to a threshold, block S32E may process the statistics for the trial index alignments to identify one of the trial index alignments for which the error rate is lowest. As long as the trial index alignments include the correct index alignment the lowest average error rate should correspond to the correct index alignment, which represents the correspondence between optical pulses 11A and optical pulses 11C.

[0140] Block S33 determines whether loop S32 requires repeating for another trial index alignment (e.g. because the correct index alignment has not yet been identified). If so, method 30 returns to block S32A). Otherwise method 30 proceeds to block S34 which outputs the correct index alignment.

[0141] In some embodiments, at least blocks S32C, S32D and S32E are performed at unit 12A and / or unit 12B. Unit 12A (or 12B as applicable) may then compare the measurement results to the information encoded in optical pulses 11 A (or 11 B as applicable) for different trial alignments and identify an index alignment that minimizes the error rate and / or corresponds to an error rate that is below a threshold.

[0142] Fig. 3A is a plot of error rate for one-click events as a function of index alignment for simulated data generated by pseudo-random number generators over a wide range of index alignments. A sharp dip 36 in error rate corresponds to the correct index alignment 37. The correct index alignment 37 corresponds to an error rate below threshold 38 and is also the lowest error rate across all of the trial index alignments.

[0143] In Fig. 3A, the number A / of qubits (optical pulses 11 A) sent by unit 12A is one million (1 E6), the probability of detection for any single optical pulse 11A is 1%, the probability that the measurement basis used in any detection will match the basis in which quantum information was encoded in an optical pulse 11A is 50%, and the incidence of errors in the detection and measurement process is 0%.

[0144] For the example of Fig. 3A, those one-click events where optical pulse 11A is lost the average error rate is 50%. For those one-click events where optical pulse 11 C is lost the average error rate is 0%. Where the one-click events are evenly divided between one-click events for which optical pulse 11A was lost and one-click events for which optical pulse 11C was lost the average error rate is expected to be 25% for a large enough number of one-click events.

[0145] The data of Fig. 3A assumes that optical pulses 11 A and optical pulses 11 C are equally likely to be lost. This assumption affects the expected error rate for the case where the index alignment is correct because results of measurements of optical pulses 11C is not expected to be correlated with quantum information encoded in optical pulses 11 A whereas results of measurements of optical pulses 11 A are expected to be correlated with the quantum information encoded in the optical pulses 11 A (as long as the optical information is encoded and the measurements are made using the same basis). If one-click events are more likely to be associated with photons of optical pulses 11C than photons of optical pulses 11 A (e.g. because optical pulses 11A have a higher probability of being lost than optical pulses 11C) then the average error rate for correct index alignment is expected to be increased relative to the case where optical pulses 11A and 11 C have equal probabilities of being lost.

[0146] The presence of additional errors e.g. bit flip errors reduces the visibility of dip 36 in the error function. As long as these additional errors do not occur at a rate that is too high a threshold 38 may be set which will reliably detect an index alignment corresponding to correct index alignment 35.

[0147] Method 30 may be varied. For example, iterations of loop S32 and / or calculations for different trial index alignments may be performed in parallel.

[0148] Returning to Fig. 2, block S30A uses the index alignment determined by block S34 to match indices of optical pulses 11A and 11C for two-click events. The two- click events are then used in block S30B, for example, in performance of a QKD protocol.

[0149] In some applications, unit 12C serves as an intermediary for executing protocols between a unit 12A and another unit 12B. For example, units 12A, 12B, and 12C may be QKD units. Unit 12C may be used to execute a QKD protocol to provide each of units 12A (playing the role of “Alice”) and 12B (playing the role of “Bob”) with a secure key that may be used for cryptographic purposes. In such applications, methods 20, 30 may be performed to establish index alignment between unit 12A and unit 12C (playing the role of “Charlie”) and performed separately to establish index alignment between unit 12B and unit 12C.

[0150] Fig. 4 is a block diagram illustrating an example apparatus 40. Apparatus 40 includes three units 12A, 12B and 12C. Apparatus 40 may, for example, be used to perform QKD with units 12A and 12B performing the roles of Alice and Bobrespectively and unit 12C performing the role of Charlie. As such, units 12A, 12B, and 12C may be provided as QKD units.

[0151] Unit 12C is in optical communication with each of units 12A and 12B by respective optical communication paths AC and 14BC. Units 12A, 12B and 12C are interconnected for data communication by a data communication network 13. Data communication network 13 may, for example, comprise a classical data communication network such as any communication network that provides wired, wireless, and / or optical communication paths operable to carry data among units 12A, 12B and 12C.

[0152] Unit 12C comprises at least one BSA. For simplicity of explanation, the illustrated unit 12C comprises three BSAs 16A, 16B and 16C (generally and collectively BSAs 16). BSAs 16 each include first and second input ports 41 , 42 and first and second photon detectors 43. Photon detectors 43 are operable to detect photons and to measure one or more characteristics of detected photons (e.g. a time bin, a polarization state or the like).

[0153] A control system 45 that includes a clock 15C and a controller 19C and an interface 47 is connected to receive output signals from detectors 43. Signal lines for carrying the output signals of detectors 43 are omitted in Fig. 4.

[0154] Unit 12C includes at least one optical port. For simplicity of explanation the illustrated unit 12C includes optical ports 44A and 44B. Optical port 44A is coupled to receive optical signals from optical path MAC and to deliver the optical signals to an input 41 of BSA 16A. Optical port 44B is coupled to receive optical signals from optical path 14BC and to deliver the optical signals to an input 41 of BSA 16B.

[0155] Unit 12C also includes a plurality of quantum memories 18. For simplicity of explanation quantum memories 18 are shown as being divided into a first group 18A and a second group 18B. First group 18A includes quantum memories 18A-0, 18A-1 , 18A-2 ... etc. Second group 18B includes quantum memories 18B-0, 18B-1 , 18B-2, ... etc. In apparatus 40, each quantum memory group 18A, 18B includes N quantum memories.

[0156] An optical switching network 46A is arranged to selectively optically couple any one of the quantum memories of group 18A either to input port 42 of BSA 16A or to input port 41 of BSA 16C. An optical switching network 46B is arranged to selectively optically couple any one of the quantum memories of group 18B either to input port 42 of BSA 16B or to input port 42 of BSA 16C. Optical switching networks46A and 46B are controlled by controller 19C of control system 45. Control system 45 also includes an interface 47 that is controlled by controller 19C. Interface 47 is operable to cause individual ones of quantum memories 18 to emit photons and to apply operations (e.g. unitary transformations) to control quantum states of individual ones of quantum memories 18. For example, interface 47 may include optical sources (e.g. lasers) and / or RF sources controllable to initialize quantum memories 18 in desired quantum states, optically drive quantum memories 18, modify the quantum states of quantum memories 18 and / or make measurements on quantum memories 18.

[0157] In some embodiments units 12A and / or 12B operate at ambient temperature (e.g. room temperature) while at least some parts of unit 12C (e.g. quantum memories 18 and / or photon detectors 43 of BSAs) operate at cryogenic temperatures.

[0158] In operation (for example to perform QKD according to the QKD protocol described in Panayi, Rzavi, Ma, & Liitkenhaus, 2014), units 12A and 12B may respectively in cooperation with unit 12C, each perform an initialization routine with unit 12C. The initialization routine involving unit 12A may, for example comprise synchronizing the clock frequency of clock 15A with that of clock 15C of unit 12C and delivering a set of optical pulses 11 A to unit 12C to enable unit 12C to determine appropriate time offsets for generating optical pulses at quantum memories of groups 18A and 18B respectively. In some embodiments separate time offsets are determined for different ones of the quantum memories of quantum memory groups 18A, 18B.

[0159] It is not necessary that, after the initialization, either of units 12A and 12B agree with unit 12C on an absolute time with sufficient precision to determine the indices of optical pulses 12A, 12B at unit 12C based solely on an agreed time at which transmission of a sequence of pulses will start at a unit 12A or 12B, the time period separating optical pulses in the series and the times of arrival of the optical pulses 12A, 12B at unit 13C.

[0160] After the initialization is complete, units 12A and 12B may each generate and send toward unit 12C a series of optical pulses (11 A, 11 B respectively) by way of optical paths AC and 14BC respectively. Units 12A and 12B may, for each optical pulse 11 A or 11 B, choose a basis, choose a classical bit value, and encode the bit value using the basis in a photonic qubit. The basis and classical bit values may bechosen randomly. The photonic qubits are emitted into optical paths AC and 14BC respectively as optical pulses 11 A and 11 B.

[0161] For each expected optical pulse 11A, control system 45 of unit 12C prepares one quantum memory of group 18A (in this example, quantum memory 18A-0) to emit an optical pulse 11C and configures optical switching network 46A to deliver the optical pulse 11C from quantum memory 18A-0 to input 42 of BSA 16A. Control system 45 causes the quantum memory to emit the optical pulse 11C at a time such that the optical pulse 11 C is present in BSA 16A substantially simultaneously with the expected time of arrival of the next optical pulse 11 A from unit 12A.

[0162] In order to visualize operation of apparatus 40 it is convenient to consider the case where unit 12C generates a first optical pulse 11 C using quantum memory 18A- 0, a second optical pulse 11 C using quantum memory 18A-1 and so-on. Control system 45 may, however, utilize the quantum memories of group 18A in any order, may re-initialize and re-use quantum memories used for one-click or zero-click events and may keep track of the source of quantum information stored in any of the quantum memories of group 18A.

[0163] If a two-click event occurs at BSA 16A then controller 45A completes quantum teleportation of the quantum state of optical pulse 11 A into the quantum memory by applying a unitary operation to the quantum memory based on results of measurements by photon detectors 43 of BSA 16A.

[0164] If a one-click or zero-click event occurs at BSA 16A then the quantum memory that was caused to emit the optical pulse 11C may be re-initialized.

[0165] Control system 45 of unit 12C may cause unit 12C to operate in a similar manner to process a sequence of optical pulses 11 B originating from unit 12B using BSA 16B and quantum memories of group 18B.

[0166] The loading of quantum information into quantum memories of groups 18A and 18B from units 12A and 12B respectively can be asynchronous. There are no requirements that sequences of optical pulses 11 A from unit 12A and sequences of optical pulses 11 B from unit 12B be delivered at the same time, at overlapping times, with the same pulse-to-pulse period, etc. In some embodiments, each of units 12A and 12B cooperates with unit 12C to perform method 20 (Fig. 2).

[0167] Once two quantum memories (for example, quantum memories 18A-P and 18B-Q where P and Q are indices) have respectively been successfully loaded with the quantum information from optical pulses 11 A and 11 B respectively, controlsystem 45 coordinates a BSM on quantum memories 11 A and 11 B. Performing the BSM may comprise: setting optical switching network 46A to direct photons from quantum memory 18A-P to input 41 of BSA 16C; setting optical switching network 46B to direct photons from quantum memory 18B-Q to input 42 of BSA 16C; and causing each of quantum memories 18A-P and 18B-Q to emit a respective photon with a timing such that the emitted photons are present substantially simultaneously at BSA 16C. Results of the BSM made by BSA 16C may then be used for QKD according to a QKD protocol.

[0168] Fig. 4A illustrates operation of apparatus 40. At block S41A an optical pulse 11A is emitted by unit 12A. At block S42A a BSM is performed on optical pulse 11A and an optical pulse 11 C emitted from a quantum memory to be loaded (in this example quantum memory 18A-P). Block S43A determines whether the BSM at block S42A succeeded. For the BSM to be successful, the BSM must correspond to a two- click event and the measurement basis used for the BSM must agree with a basis in which quantum information was encoded in optical pulse 11 A. If block S43A determines that the BSM was successful, block S44A applies an operation to adjust the quantum state of quantum memory 18A-P. The operation may be based on a result of the BSM of block S42A. The operation of block S44A completes loading of quantum information from optical pulse 11A into quantum memory 18A-P as indicated at block S46A.

[0169] Blocks S41 B, S42B, S43B, S44B operate to complete loading of quantum information from an optical pulse 11 B emitted from unit 12B into quantum memory 18B-Q as indicated at block S46B analogously to blocks S41A, S42A, S43A, S44A and S46A.

[0170] Block S47 determines whether quantum memories 18A-P and 18B-Q are both successfully loaded. If so, Block S48 performs a BSM between quantum memories 18A-P and 18B-Q. A result of the BSM of block S48 may be distributed (e.g. to one or both of units 12A and 12B). The BSM result is communicated back to units 12A and 12B, for example by communication network 13. Each of units 12A and 12B may use the BSM result to generate one bit of raw key. This process may be repeated until a raw key of a desired length that is shared by units 12A and 12C has been generated.

[0171] Fig. 5 is a schematic illustration showing an example apparatus 50 according to some embodiments of the invention. Apparatus 50 differs from apparatus 40 in that unit 12C is replaced with unit 12D. Unit 12D is constructed to measure pairs of photonstates originating from units 12A and 12B directly in a BSA 16. Unit 12D does not require quantum memories 18.

[0172] Apparatus 50 may, for example, be applied for measurement device independent QKD (MDI-QKD). As known in the art, in MDI-QKD results of measurements on pairs of photon states originating from different sources (traditionally “Alice” and “Bob”, in this example, unit 12A corresponds to Alice and unit 12B corresponds to Bob) are shared with at least one of Alice and Bob. The measurement results allow Alice to know whether the information Bob encoded in a photon state sent to be measured at unit 12C was the same as or different from the information Alice encoded in a corresponding photon state sent to unit 12C. For this to work it is necessary to know for each photon state sent by Alice, which photon state sent by Bob corresponds to (i.e. was measured together with) that photon state sent by Alice. The index alignment methods described herein (e.g. method 30 of Fig. 3) may be used to determine the correct index alignment.

[0173] For example, units 12A and 12B may respectively emit optical pulses 11A and 11 B with a timing such that pairs of optical pulses 11 A and 11 B are present at BSA 16 of unit 12D substantially simultaneously. Controller 19C of unit 12D may be configured to monitor outputs of BSA 16 to identify one-click events and two-click events. Controller 19C may make available results of the one-click events, indices assigned to the one-click events at unit 12D and a basis with which BSA 16 was aligned for each of the one-click events to each of units 12A and 12B. Each of units 12A and 12B may then perform method 30 to determine an index alignment relative to the indices assigned by unit 12D. Units 12A and 12B may share their index alignments. In some embodiments units 12A and 12B subsequently use results of the two-click events to generate a shared encryption key.

[0174] From the foregoing it can be understood that the methods and apparatus described herein are advantageous in cases where optical connections 14 AC, 14BC have limited availability and / or limited capacity. When using the present apparatus and methods it is not necessary to transmit optical pulses that are dedicated to index alignment. Using results of one-click events (information that is typically discarded as being useless) to facilitate index alignment does not consume information that is useful for QKD using a MA-QKD (memory-assisted-QKD) or MDI-QKD (measurement device independent-QKD) protocol. Furthermore, the present methods and apparatus do not require absolute time agreement between participating units 12A, 12B and12C.

[0175] Apparatus as described herein includes controllers and control systems (e.g. 19A, 19B, 19C, 45). Such controllers and control systems may be implemented in a wide variety of ways, for example, by specifically designed hardware, configurable hardware, programmable data processors configured by the provision of software (which may optionally comprise “firmware”) capable of executing on the data processors, special purpose computers or data processors that are specifically programmed, configured, or constructed to perform one or more steps in a method as explained in detail herein and / or combinations of two or more of these. Examples of specifically designed hardware are: logic circuits, application-specific integrated circuits (“ASICs”), large scale integrated circuits (“ LSI s”), very large scale integrated circuits (“VLSIs”), and the like. Examples of configurable hardware are: one or more programmable logic devices such as programmable array logic (“PALs”), programmable logic arrays (“PLAs”), and field programmable gate arrays (“FPGAs”). Examples of programmable data processors are: microprocessors, digital signal processors (“DSPs”), embedded processors, graphics processors, math coprocessors, general purpose computers, server computers, cloud computers, mainframe computers, computer workstations, and the like. For example, one or more data processors in a control circuit for a device may implement methods as described herein by executing software instructions in a program memory accessible to the processors.

[0176] The methods and apparatus described herein may be varied. For example:• For ease of explanation, Fig. 4 shows memories of apparatus 40 being segregated into groups 18A and 18B. This is not required. Control system 45 may assign quantum memories to receive loading of quantum information and keep track of those assignments without the quantum memories having been initially assigned to separate groups.• Optical switching to facilitate the operations described herein (performing BSMs, loading quantum information) may be performed with a wide variety of configurations of optical switches which are not necessarily divided into separate optical switching networks 46A and 46B.• Apparatus for performing the methods described herein may incorporate more of fewer BSAs than are shown in the provided examples. For example, optical switches may be provided to selectively provide optical pulses 11 A and opticalpulses 11 B to the same BSA (at different times) rather than providing separate BSAs 16A and 16B as shown in Fig. 4).These examples are intended to be illustrative examples of a few possible variations and are not intended to be exhaustive.

[0177] Where a component (e.g. a controller, BSA, photon detector, switching network, optical connection, data communication network, assembly, device, etc.) is referred to herein, unless otherwise indicated, reference to that component (including a reference to a “means”) should be interpreted as including as equivalents of that component any component which performs the function of the described component (i.e. , that is functionally equivalent), including components which are not structurally equivalent to the disclosed structure which performs the function in the illustrated exemplary embodiments of the invention.

[0178] Processing may be centralized or distributed. Where processing is distributed, information including software and / or data may be kept centrally or distributed. Such information may be exchanged between different functional units by way of a communications network, such as a Local Area Network (LAN), Wide Area Network (WAN), or the Internet, wired or wireless data links, electromagnetic signals, optical signals, or other data communication channel.

[0179] The invention may also be provided in the form of a program product. The program product may comprise any non-transitory medium which carries a set of computer-readable instructions which, when executed by a data processor, cause the data processor to execute a method of the invention (e.g. method 30 or method 20 or parts of these methods). Program products according to the invention may be in any of a wide variety of forms. The program product may comprise, for example, non- transitory media such as magnetic data storage media including floppy diskettes, hard disk drives, optical data storage media including CD ROMs, DVDs, electronic data storage media including ROMs, flash RAM, EPROMs, hardwired or preprogrammed chips (e.g., EEPROM semiconductor chips), nanotechnology memory, or the like. The computer-readable signals on the program product may optionally be compressed or encrypted.

[0180] In some embodiments, the invention may be implemented in software. For greater clarity, “software” includes any instructions executed on a processor, and may include (but is not limited to) firmware, resident software, microcode, code for configuring a configurable logic circuit, applications, apps, and the like. Bothprocessing hardware and software may be centralized or distributed (or a combination thereof), in whole or in part, as known to those skilled in the art. For example, software and other modules may be accessible via local memory, via a network, via a browser or other application in a distributed computing context, or via other means suitable for the purposes described above.Interpretation of Terms

[0181] Unless the context clearly requires otherwise, throughout the description and the claims:• “comprise”, “comprising”, and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”;• “unit” means a functional unit. A unit may be but is not necessarily portable. A unit may be but is not necessarily contained in a single housing. In some embodiments, a unit or at least main physical components of the unit is located at a specific location (e.g. a building or address).• “connected”, “coupled”, or any variant thereof, means any connection or coupling, either direct or indirect, between two or more elements; the coupling or connection between the elements can be physical, logical, or a combination thereof;• “herein”, “above”, “below”, and words of similar import, when used to describe this specification, shall refer to this specification as a whole, and not to any particular portions of this specification;• “or”, in reference to a list of two or more items, covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list;• the singular forms “a”, “an”, and “the” also include the meaning of any appropriate plural forms. These terms (“a”, “an”, and “the”) mean one or more unless stated otherwise;• “and / or” is used to indicate one or both stated cases may occur, for example A and / or B includes both (A and B) and (A or B);• “approximately” when applied to a numerical value means the numerical value ± 10%;• where a feature is described as being “optional” or “optionally” present ordescribed as being present “in some embodiments” it is intended that the present disclosure encompasses embodiments where that feature is present and other embodiments where that feature is not necessarily present and other embodiments where that feature is excluded. Further, where any combination of features is described in this application this statement is intended to serve as antecedent basis for the use of exclusive terminology such as "solely," "only" and the like in relation to the combination of features as well as the use of "negative" limitation(s)” to exclude the presence of other features; and• “first” and “second” are used for descriptive purposes and cannot be understood as indicating or implying relative importance or indicating the number of indicated technical features.

[0182] Words that indicate directions such as “vertical”, “transverse”, “horizontal”, “upward”, “downward”, “forward”, “backward”, “inward”, “outward”, “left”, “right”, “front”, “back”, “top”, “bottom”, “below”, “above”, “under”, and the like, used in this description and any accompanying claims (where present), depend on the specific orientation of the apparatus described and illustrated. The subject matter described herein may assume various alternative orientations. Accordingly, these directional terms are not strictly defined and should not be interpreted narrowly.

[0183] Where a range for a value is stated, the stated range includes all sub-ranges of the range. It is intended that the statement of a range supports the value being at an endpoint of the range as well as at any intervening value to the tenth of the unit of the lower limit of the range, as well as any subrange or sets of sub ranges of the range unless the context clearly dictates otherwise or any portion(s) of the stated range is specifically excluded. Where the stated range includes one or both endpoints of the range, ranges excluding either or both of those included endpoints are also included in the invention.

[0184] Certain numerical values described herein are preceded by "about". In this context, "about" provides literal support for the exact numerical value that it precedes, the exact numerical value ±5%, as well as all other numerical values that are near to or approximately equal to that numerical value. Unless otherwise indicated a particular numerical value is included in “about” a specifically recited numerical value where the particular numerical value provides the substantial equivalent of the specifically recited numerical value in the context in which the specifically recitednumerical value is presented. For example, a statement that something has the numerical value of “about 10” is to be interpreted as: the set of statements:• in some embodiments the numerical value is 10;• in some embodiments the numerical value is in the range of 9.5 to 10.5; and if from the context the person of ordinary skill in the art would understand that values within a certain range are substantially equivalent to 10 because the values with the range would be understood to provide substantially the same result as the value 10 then “about 10” also includes:• in some embodiments the numerical value is in the range of C to D where C and D are respectively lower and upper endpoints of the range that encompasses all of those values that provide a substantial equivalent to the value 10.

[0185] Specific examples of systems, methods and apparatus have been described herein for purposes of illustration. These are only examples. The technology provided herein can be applied to systems other than the example systems described above. Many alterations, modifications, additions, omissions, and permutations are possible within the practice of this invention. This invention includes variations on described embodiments that would be apparent to the skilled addressee, including variations obtained by: replacing features, elements and / or acts with equivalent features, elements and / or acts; mixing and matching of features, elements and / or acts from different embodiments; combining features, elements and / or acts from embodiments as described herein with features, elements and / or acts of other technology; and / or omitting combining features, elements and / or acts from described embodiments.

[0186] As will be apparent to those of skill in the art upon reading this disclosure, each of the individual embodiments described and illustrated herein has discrete components and features which may be readily separated from or combined with the features of any other described embodiment(s) without departing from the scope of the present invention.

[0187] Any aspects described above in reference to apparatus may also apply to methods and vice versa.

[0188] Any recited method can be carried out in the order of events recited or in any other order which is logically possible. For example, while processes or blocks arepresented in a given order, alternative examples may perform routines having steps, or employ systems having blocks, in a different order, and some processes or blocks may be deleted, moved, added, subdivided, combined, and / or modified to provide alternative or subcombinations. Each of these processes or blocks may be implemented in a variety of different ways. Also, while processes or blocks are at times shown as being performed in series, these processes or blocks may instead be performed in parallel, simultaneously or at different times.

[0189] Various features are described herein as being present in “some embodiments”. Such features are not mandatory and may not be present in all embodiments. Embodiments of the invention may include zero, any one or any combination of two or more of such features. All possible combinations of such features are contemplated by this disclosure even where such features are shown in different drawings and / or described in different sections or paragraphs. This is limited only to the extent that certain ones of such features are incompatible with other ones of such features in the sense that it would be impossible for a person of ordinary skill in the art to construct a practical embodiment that combines such incompatible features. Consequently, the description that “some embodiments” possess feature A and “some embodiments” possess feature B should be interpreted as an express indication that the inventors also contemplate embodiments which combine features A and B (unless the description states otherwise or features A and B are fundamentally incompatible). This is the case even if features A and B are illustrated in different drawings and / or mentioned in different paragraphs, sections or sentences.

[0190] It is therefore intended that the following appended claims and claims hereafter introduced are interpreted to include all such modifications, permutations, additions, omissions, and sub-combinations as may reasonably be inferred. The scope of the claims should not be limited by the preferred embodiments set forth in the examples, but should be given the broadest interpretation consistent with the description as a whole.

Claims

WHAT IS CLAIMED IS:1 . A method for determining correspondence between optical pulses sent by a first unit and optical pulses received from the first unit at a second unit, the first unit emitting a first series of first unit optical pulses into an optical path that is arranged to deliver the first unit optical pulses to the second unit, each of the first unit optical pulses encoding information in a photon state of the first unit optical pulse; the method comprising: at the second unit, attempting to perform Bell state measurements (BSMs) between the first unit optical pulses and optical pulses of a second series of optical pulses; recording results of the attempted BSMs, the recorded results including at least some results which correspond to one-click events; determining an error rate for each of plural trial index alignments between the first unit optical pulses and the second series of optical pulses based at least in part on the results which correspond to one-click events; and selecting, from the plural trial index alignments, one of the plural trial index alignments which minimizes the error rate and / or corresponds to the error rate being below a threshold, as an index alignment representing the correspondence between the first unit optical pulses emitted by the first unit and the first unit optical pulses of the attempted BSMs.

2. The method according to claim 1 wherein the optical path is lossy and a success rate for transmission of the first unit optical pulses to the second unit is 20% or less.

3. The method according to claim 1 or 2 comprising transmitting the recorded results of those of the attempted BSMs which correspond to one-click events to the first unit and performing determining the error rate for each of the plural trial index alignments at the first unit.

4. The method according to any of claims 1 to 3 wherein the information encoded in the photon states of the first unit optical pulses is bit values.

5. The method according to claim 4 wherein, for each of the first unit optical pulses the bit value is represented in a corresponding first unit basis selected from a plurality of bases and wherein the attempted BSMs are each performed in a corresponding second unit basis included in the plurality of bases and the method comprises, in determining the error rates for the plural trial index alignments, ignoring the results of those of the attempted BSMs which correspond to one-click events for which the corresponding first unit basis does not match the corresponding second unit basis.

6. The method according to claim 5 wherein the second unit basis is the same for all of the attempted BSMs.

7. The method according to claim 5 wherein the second unit basis is selected from the plurality of bases and different ones of the attempted BSMs are performed in different ones of the plurality of bases.

8. The method according to any of claims 4 to 7 comprising randomly or pseudo- randomly selecting the bit value for each of the first unit optical pulses.

9. The method according to any of claims 1 to 8 comprising, at the second unit, determining a time offset relative to arrival times of the first unit optical pulses at the second unit such that the optical pulses of the second series of optical pulses and the first unit optical pulses arrive at a BSA of the second unit substantially simultaneously.

10. The method according to any of claims 1 to 9 wherein the first unit optical pulses are emitted at a rate of at least 1 MHz.11 . The method according to any of claims 1 to 10 wherein the encoding of the information in the first unit optical pulses comprises an encoding selected from the group consisting of: time-bin encoding, polarization encoding, spatial frequency bin encoding, time-frequency mode encoding and combinations thereof.

12. The method according to any of claims 1 to 11 wherein the encoding of the information in the first unit pulses comprises encoding in a higher dimensional photonstate having two or more dimensions.

13. The method according to any of claims 1 to 12 wherein each of the first unit optical pulses is constituted by a single photon.

14. The method according to any of claims 1 to 13 wherein at least some of the first unit optical pulses is constituted by a coherent superposition of quantum states.

15. The method according to any of claims 1 to 14 wherein the optical pulses of the second series of optical pulses are emitted from a quantum memory of the second unit.

16. The method according to claim 15 comprising: identifying those of the attempted BSMs between the first unit optical pulses and the optical pulses of the second series of optical pulses which correspond to two- click events and for each of such two-click events attempting to load the encoded information of the corresponding first unit optical pulse into the quantum memory of the second unit.

17. The method according to claim 16 comprising: determining correspondence between optical pulses sent by a third unit and optical pulses received from the third unit at the second unit by: at the third unit emitting a series of third unit optical pulses into an optical path configured to deliver the third unit optical pulses to the second unit, each of the third unit optical pulses encoding quantum information; at the second unit attempting to perform a BSM between each of the third unit optical pulses emitted by the third unit and second unit optical pulses emitted from another quantum memory of the second unit; recording results of those of the attempted BSMs between the third unit optical pulses and the second unit optical pulses which correspond to one-click events; determining an error rate for each of plural trial index alignments between the third unit optical pulses and the attempted BSMs between the third unit optical pulses and the second unit optical pulses; and selecting one of the trial index alignments between the third unit optical pulsesand the attempted BSMs between the third unit optical pulses and the second unit optical pulses which has a minimum error rate and / or for which the error rate is below a threshold as an index alignment representing the correspondence between the third unit optical pulses sent by the third unit and the attempted BSMs between the third unit optical pulses and the second unit optical pulses.

18. The method according to claim 17 wherein, for each of the third unit optical pulses the encoded information comprises a bit value represented in a corresponding third unit basis of the plurality of bases and wherein the attempted BSMs between the third unit optical pulses and the second unit optical pulses are performed in a corresponding second unit basis selected from the plurality of bases and the method comprises identifying those of the attempted BSMs between the third unit optical pulses and the second unit optical pulses which correspond to two-click events for which the corresponding third unit basis matches the corresponding second unit basis using the index alignment which represents the correspondence between the third unit optical pulses sent by the third unit and the attempted BSMs between the third unit optical pulses and the second unit optical pulses.

19. The method according to claim 17 or 18 comprising: identifying those of the attempted BSMs between the third unit optical pulses and the second unit optical pulses which correspond to two-click events and for each of such two-click events attempting to load the encoded information of the corresponding third unit optical pulse into the corresponding additional quantum memory of the second unit; for each of a plurality of pairs of the quantum memories of the second unit, where each of the pairs includes one of the quantum memories into which the encoded information of one of the first unit optical pulses has been loaded and one of the quantum memories into which the encoded information of one of the third unit optical pulses has been loaded performing a Bell state measurement on the pair of quantum memories.

20. The method according to claim 19 comprising making available results of the Bell state measurements on the pairs of quantum memories to at least one of the first unit and the third unit.21 . The method according to any of claims 1 to 16 wherein the optical pulses of the second series of optical pulses are third unit optical pulses generated at a third unit and optically transmitted from the third unit to the second unit.

22. The method according to claim 21 wherein the third unit optical pulses each encode information and the method comprises: determining correspondence between the third unit optical pulses sent by the third unit and the first series of optical pulses, respectively received from the third unit and first unit at the second unit by: determining an error rate for each of plural trial index alignments between the third unit optical pulses and the first series of optical pulses; and selecting one of the trial index alignments between the third unit optical pulses and the first series of optical pulses which corresponds to a smallest error rate and / or corresponds to an error rate below a threshold as an index alignment representing the correspondence between the third unit optical pulses and the first series of optical pulses.

23. The method according to any of claims 1 to 22 wherein some or all of the BSMs are successful BSMs and the method comprises using results of the successful BSMs for quantum key distribution.

24. A method for determining correspondence between first unit optical pulses originating at a first unit that contain information encoded in photon states of the first unit optical pulses and optical pulses received from the first unit at a second unit, the method comprising: obtaining data comprising measurement results of attempted Bell state measurements (BSMs) performed at the second unit between the first unit optical pulses and optical pulses of a second series of optical pulses, the measurement results including results corresponding to one-click events; using data that comprises the information encoded in the first unit optical pulses, determining, based on at least the one-click events, an error rate for each of plural trial index alignments between the first unit optical pulses originating at the first unit and the attempted BSMs; andselecting one of the trial index alignments which minimizes the error rate and / or corresponds to the error rate being below a threshold, as an index alignment representing the correspondence between the first unit optical pulses originating at the first unit and the first unit optical pulses of the attempted BSMs.

25. The method according to claim 24 comprising using measurement results of those of the attempted BSMs that correspond to two-click events for quantum key distribution.

26. A system operable to determine correspondence between optical pulses sent by a first unit and optical pulses received from the first unit at a second unit, the first unit emitting a first series of first unit optical pulses, each of the first unit optical pulses carrying information encoded in a photon state of the first unit optical pulse; the second unit comprising: a Bell state analyzer (“BSA”); at least one optical port optically connectible to the BSA; and ; a control system including a controller, the controller operative to: determine an error rate for each of plural trial index alignments between the first series of optical pulses and the second series of optical pulses, based on results of measurements by the BSA corresponding to attempted Bell state measurements (“BSMs”) between the first unit optical pulses and optical pulses of a second series of optical pulses, wherein at least some of the results of measurements correspond to one-click events; and select from the plural trial index alignments one of the plural trial index alignments which minimizes the error rate and / or corresponds to an error rate below a threshold, as an index alignment representing the correspondence between the first unit optical pulses sent by the first unit and the first unit optical pulses of the attempted BSMs.

27. A system for determining correspondence between first unit optical pulses originating at a first unit that contain information encoded in photon states of the first unit optical pulses and optical pulses originating from the first unit that are received at a second unit, the system comprising a data processor configured to: process data that comprises the information encoded in the first unit opticalpulses; and data comprising results of attempted Bell state measurements (BSMs) performed at the second unit between the first unit optical pulses that are received at the second unit and optical pulses of a second series of optical pulses, where the results of the attempted BSMs comprise results of BSMs that correspond to one-click events, the processing comprising: determining an error rate for each of plural trial index alignments between the first series of optical pulses and the attempted BSMs; and selecting one of the trial index alignments which minimizes the error rate and / or corresponds to the error rate being below a threshold, as an index alignment representing the correspondence between the first unit optical pulses sent by the first unit and the first unit optical pulses of the attempted BSMs.

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