JP5534568B2 - Quantum communication method, quantum communication system, and receiver - Google Patents

Description

  The present invention relates to a quantum communication technique including a step of preparing a quantum system in a certain quantum state on the transmitter side and sending the quantum system to the receiver side, and a step of performing quantum measurement on the quantum system on the receiver side.

In the present specification, the quantum system, the behavior refers to a system described by quantum theory, for example photons, electrons, and other particles, atoms, include C ₆₀ fullerene other molecules.

  In this specification, PVM is an abbreviation for Projection Valued Measure, and refers to POVM composed of projection operators whose elements are orthogonal to each other. Projection measurement refers to quantum measurement in which the measurement operator is described in PVM. Note that POVM is an abbreviation of Positive Operator Valued Measure, and is a set of operators (operators) that satisfy both positive value and completeness. An operator constituting a set such as PVM or POVM is also called an element.

  Non-Patent Document 1 is a commercially available general textbook in this technical field. The above terms and their definitions are as described in Non-Patent Document 1.

  Non-Patent Document 2 discloses a BB84 (Bennett Brassard 84) protocol that is now widely known as a quantum communication technique. Hereinafter, without limitation, the BB84 protocol will be outlined by taking as an example the case where the quantum system is a photon as a two-level system and the quantum state is the polarization state of the photon.

  As a premise, the sender and the receiver determine a certain first PVM and a second PVM composed of elements that are not orthogonal to the elements of the first PVM. Here, a case where the first PVM has | H> <H | and | V> <V | as elements and the second PVM has | R> <R | and | L> <L | To do.

  Where | H> is a horizontal linear polarization state, | V> is a vertical linear polarization state, | R> is a clockwise circular polarization state, and | L> is a counterclockwise circular polarization state in Dirac bracket notation. It is a thing. Each element of the first and second PVMs is a measurement operator and also a polarization state expressed by a density operator.

  FIG. 7 shows a conceptual diagram of a quantum communication system that implements the BB84 protocol. A transmitting device 20 arranged on the sender side and a receiving device 21 arranged on the receiver side are connected by a quantum channel 22 and a public channel 23.

  In the transmission device 20, the photon emitter 24 includes a sum set {| H> <H |, | V> <V |, | R> <R |, | L> <L |} of the first and second PVMs. The photons prepared in the polarization state selected at random are sequentially emitted to the receiving device 21 through the quantum channel 22.

  The transmitter computer 25 stores the identification information for identifying each photon emitted from the photon emitter 24 in association with the polarization state of the photon. Here, the identification information is specifically time slot information indicating the order in which the photons are emitted from the photon emitter 24.

  Since the elements of the first PVM and the second PVM are non-orthogonal, the receiving device 21 has four states of | H>, | V>, | R>, and | L> with respect to the acquired photons. It does not make sense to perform quantum measurement (POVM measurement) to determine which one of them corresponds. That is, from the measurement result, it cannot be said that there is any definiteness about the polarization state prepared by the photon emitter 24.

  Therefore, in the receiving device 21, the acquired photons are randomly incident on one of the first and second projection measuring devices 27 and 28 by the distributor 26. The first projection measuring device 27 performs projection measurement based on the first PVM, that is, determines whether | H> or | V>. The second projection measuring device 28 performs projection measurement based on the second PVM, that is, determines whether | R> or | L>.

  When the sorter 26 selects the correct PVM, that is, the same PVM to which the polarization state prepared by the photon emitter 24 belongs, as the basis, the polarization state prepared by the photon emitter 24 is determined from the result of the projection measurement. You can know correctly. The sorter 26 can select the correct base with a probability of 50%.

  The receiver-side computer 29 stores the identification information for identifying each photon in association with the PVM (first or second PVM) used as the basis of the projection measurement and the projection measurement result. Note that the time slot of each photon is synchronized between the transmitting device 20 and the receiving device 21, and the same photon can be identified by both.

  After the photon transmission and the projection measurement are repeated many times as described above, the receiver computer 29 uses the PVM used as the basis for the projection measurement of each photon through the public channel 23 to the sender computer. 25. The projection measurement result itself is not informed.

  On the other hand, the sender-side computer 25 checks whether the PVM notified of each photon matches the PVM to which the polarization state prepared by the photon emitter 24 belongs for that photon. The event identification information is extracted, and the response is sent to the recipient computer 29 through the public channel 23.

  When the receiver-side computer 29 can identify the event in which the PVM matches between the sender and the receiver by the answer, the polarization state prepared by the photon emitter 24 corresponds to which element of the PVM in the projection measurement result of each event. You can identify at the same time. Thereby, 1-bit information is transmitted to the receiver side in each event.

  In the event that the PVM does not match between the sender and the receiver, that is, the event in which the distributor 26 selects a PVM that is different from the PVM to which the polarization state prepared by the photon emitter 24 belongs, the photon emitter 24 is prepared. No information can be obtained from the projection measurement results regarding the polarization state. Accordingly, the projection measurement result data is discarded.

  As described above with reference to the system of FIG. 7, the essence of BB84 is as follows. (I) The elements in one PVM are different regardless of whether the execution subject of each process is a system or a human being. Since orthogonal measurement is performed on a quantum system prepared for a certain quantum state, when the projection measurement based on the PVM including the quantum state as an element is performed, the quantum state is always obtained as a measurement result, and (Ii) Since the elements of the first PVM and the second PVM are non-orthogonal, a projection measurement based on the other PVM is performed on the quantum system prepared in the quantum state represented by the element of one PVM. Even if it is performed, the natural law (quantum mechanics) that the deterministic information about the quantum state of the quantum system cannot be obtained in principle from the measurement result is used.

JP 2013-108806 A

Satoshi Ishizaka et al. "Introduction to Quantum Information Science", First Edition, Kyoritsu Publishing Co., Ltd., June 10, 2012, p.117-120 C.H.Bennett, G.Brassard, “QuantumCryptography: Public Key Distribution and Coin Tossing”, Proceedingsof IEEE International Conference on Computers Systems and Signal Processing, Bangalore India, pp.175-179 (1984) Y. Aharonov et al., Phys. Rev. Lett. 60, 1351 (1988) Masao Kitano, “Basics of Quantum Mechanics”, first edition, Kyoritsu Publishing Co., Ltd., January 30, 2010, p.184-185 G.J.Pryde et al. “Measurement of QuantumWeak Values of Photon Polarization” Phys. Rev. Lett. 94, 220405 (2005) Kazuhiro Yokota and Nobuyuki Imoto, “Observation of Hardy's Paradox by Weak Quantum Measurement”, Journal of the Physical Society of Japan, Vol. 65, No. 8 (2010) Masataka Iinuma et al. “Weak measurement of photonpolarization by back-action-induced path interference” New J. Phys. 13, 033041 (2011)

  In quantum communication, information transmission cannot be realized simply by transmitting a quantum system from the sender side to the receiver side.

  The BB84 protocol requires the receiver to report to the sender the PVM that he has chosen as the basis for the projection measurement for each photon acquired from the sender. In addition, the sender also needs to confirm and answer for each photon whether or not the receiver has selected the correct PVM. For this reason, classical communication between the sender and the receiver becomes complicated.

  In this specification, classical communication refers to communication between a transmitter and a receiver that is performed accompanying transmission of a quantum system in order to realize information transmission using the quantum system. In the example of FIG. 7, the communication between both computers 25 and 29 through the public channel 23 is classical communication. However, classical communication is a concept that does not depend on the physical entity of the channel (communication channel) to be used. For example, classical communication and quantum transmission may share the same channel.

  While research to increase safety against eavesdropping is underway, a simple quantum communication technology that does not require as strict procedures as the BB84 protocol is also desired.

  An object of the present invention is to provide a quantum communication technique in which accompanying classical communication is difficult to complicate.

  The inventor of the present application has found that the above object can be achieved by using weak measurement.

  As disclosed in Non-Patent Documents 3 and 4, weak measurement itself is already known.

  As disclosed in Non-Patent Documents 5 to 7 and Patent Document 1, various examples of weak measurement have been studied by those skilled in the art. However, no example of applying weak measurement to quantum communication in the following aspect of the present invention has been found.

According to one aspect of the present invention, (a) a transmission apparatus includes a first PVM determined in advance between a sender and a receiver and a second PVM formed of elements that are not orthogonal to the elements of the first PVM. A step of sequentially sending a quantum system prepared in a quantum state represented by an element randomly selected from a union to a receiving device, and (b) the receiving device for each of the quantum systems acquired from the transmitting device, the the first projective measurement and it first weak value of the last measurement, as well as the second projection measurements to base the second PVM and it final measurement to base the first PVM 2 The first weak measurement is performed when the quantum state of the quantum system acquired from the transmission device belongs to the second PVM. A non-degenerate observer of the second PVM as a set of eigenstates The second weak measurement is performed for a bubble, and the quantum system obtained from the transmitting device belongs to the first PVM, and the degenerate observable with the first PVM as a set of eigenstates. (C) a step in which the transmitting device notifies the receiving device of an identification information group that specifies a plurality of quantum systems sent in the same quantum state among the quantum systems sent in the step (a); d) The receiving apparatus obtains the statistical distribution of the projection measurement result and the weak value obtained from the weak measurement result in the step (b) for each quantum system corresponding to the identification information group, and obtains the statistical distribution and the weak value obtained. quantum communication method including the step that identifies the same quantum state with is provided.

According to another aspect of the present invention, the first PVM predetermined between the sender and the receiver and the first PVM element are randomly selected from the union of the second PVM including non-orthogonal elements. The quantum system emitter prepares a quantum system emitter that emits one after another by preparing a quantum system in the quantum state represented by the element and identification information that identifies each quantum system emitted from the quantum emitter. A first computer that uses the first PVM as a basis and a final measurement for a quantum system incident on the sender computer that stores the quantum state of the quantum system in association with each other. 1 weak measurement is performed, and when the quantum state of the quantum system incident on the first weak measurement belongs to the second PVM, there is no degeneracy with the second PVM as a set of eigenstates. Configured to be done about observable A first continuous measurement instrument was for quantum systems which enters the self performs second projection measurements to base the second PVM and second weak measurements it with the final measurement, the first When the quantum state of the quantum system incident on itself belongs to the first PVM, the weak measurement of 2 is configured to be performed for an undegenerate observable having the first PVM as a set of eigenstates. A second continuous measuring device, and a distributor that randomly injects each quantum system emitted from the quantum system emitting device into either the first continuous measuring device or the second continuous measuring device, A receiver-side computer communicably connected to the sender-side computer, each quantum system emitted from the quantum-system emitter on the receiver side in correspondence with the identification information in the sender-side computer Identify to identify Information, the function of storing the measurement results of the first or second continuous measuring device in association with the quantum system, and the quantum system emitted from the quantum-system emitter from the sender-side computer When a plurality of identification information groups specifying a plurality of light emitted in the same quantum state are transmitted, the projection measurement is performed by the first and second continuous measuring devices for each quantum system corresponding to the identification information group. seeking Yowachi obtained from the statistical distribution and weak measurement results, even quantum communication system comprising a receiver-side computer having a function to identify the same quantum state using the statistical distribution and Yowachi determined Provided.

  On the receiver side, at least whether the common quantum state used for extracting the identification information group on the sender side belongs to the first or second PVM from the statistical distribution of the projection measurement result. sell. Even in the event that the projection measurement base is wrongly selected, an observable weak measurement with the correct PVM as a set of eigenstates is performed. Therefore, which element of the specified PVM is determined from the weak value by the common quantum. The state can be further narrowed down.

Thus, if the quantum system is an N level system (where N is a natural number of 2 or more), 1 + log ₂ N bits of information can be transmitted for each notification of the identification information group. When transmitting information, it is not necessary to check the PVM between the sender and receiver for each quantum system, so that the complexity of classical communication is alleviated.

1 is a conceptual diagram of a quantum communication system according to an embodiment of the present invention. (A) is a conceptual diagram of data stored in the sender computer, and (b) is a conceptual diagram of data stored in the receiver computer. 3 is a flowchart of a quantum communication method according to an embodiment of the present invention. It is a conceptual diagram which illustrates the histogram of a projection measurement result. It is the schematic which shows the structural example of a 1st continuous measuring device. It is the schematic which shows the structural example of a 2nd continuous measuring device. It is a conceptual diagram of the conventional quantum communication system.

  FIG. 1 shows a conceptual diagram of a quantum communication system according to an embodiment of the present invention. A transmitter 1 is arranged on the sender side, and a receiver 2 is arranged on the receiver side.

  The transmitter 1 includes a photon emitter 4 as a quantum emitter and a transmitter computer 5. The receiving device 2 includes a sorting device 6, a first continuous measuring device 7, a second continuous measuring device 10, and a receiver computer 13.

  The photon emitter 4 and the distributor 6 are connected by the quantum channel 3. The quantum channel 3 is composed of, for example, an optical fiber or a free space.

  The sender computer 5 and the receiver computer 13 are connected by the public channel 14. The public channel 14 is composed of, for example, a telephone line or an internet line.

  Hereinafter, a quantum communication method according to an embodiment of the present invention will be described.

  As a premise, a first PVM and a second PVM made up of elements that are not orthogonal to the elements of the first PVM are determined in advance between the sender and the receiver. All elements of one PVM of the first and second PVMs are mutually unbiased with respect to any element of the other PVM.

  In the present embodiment, it is assumed that the first PVM includes | H> <H | and | V> <V |, and the second PVM includes | R> <R | and | L> <L |. Each element of the first and second PVMs is a measurement operator and also a polarization state expressed by a density operator.

  The photon emitter 4 is randomly selected from the union {| H> <H |, | V> <V |, | R> <R |, | L> <L |} of the first and second PVMs. Photons are prepared in the polarization state and emitted one after another. The emitted photons enter the sorter 6 through the quantum channel 3.

  For example, the photon emitter 4 includes an entanglement source that emits one of the entangled photon pairs to the distributor 6 and the other to the sender side, and a union of the first and second PVMs for the other photon. And a POVM measuring device that performs POVM measurement described in POVM.

  FIG. 2A is a conceptual diagram of data stored in the sender computer 5. Each time a photon is emitted from the photon emitter 4, the transmitter computer 5 associates the photon with the identification information for identifying the photon, and stores the polarization state of the photon prepared by the photon emitter 4 in its own memory. To remember.

  Specifically, the identification information is time slot information indicating the time or order in which photons are emitted from the photon emitter 4. When photons are sequentially emitted from the photon emitter 4 at certain time intervals, each photon can be identified if the order in which the photons are emitted can be specified.

  Returning to FIG. 1, the description will be continued. The sorter 6 causes each photon acquired from the photon emitter 4 to randomly enter one of the first and second continuous measuring devices 7 and 10. For example, the distributor 6 can include an optical deflector such as an acousto-optic deflector or an electro-optic deflector.

  The first continuous measuring instrument 7 includes a first projection measuring instrument 8 and a first weak measuring instrument 9. The first projection measuring device 8 performs projection measurement based on the first PVM (hereinafter referred to as first projection measurement), that is, a determination as to whether the polarization state is | H> or | V>. Do.

The first weak measuring device 9 performs weak measurement with the first projection measurement as the final measurement . In the weak measurement, when the polarization state of a photon incident on the first continuous measuring device 7 belongs to the second PVM, the degenerate observable (hereinafter referred to as the first degenerate state) having the second PVM as a set of eigenstates. 2). In the present embodiment, the Pauli operator σ _Y is employed as the second observable.

  If the polarization state of the photon incident on the first continuous measuring instrument 7 belongs to the first PVM, the first projection measuring instrument 8 can correctly know the polarization state. The measurement result of one weak measuring device 9 may not be used. Therefore, in that case, what kind of weak measurement the first weak measuring device 9 performs is arbitrary. As long as it is a weak measurement, the disturbance that the weak measurement act gives to the polarization state of the photon to be measured is so small that it can be ignored.

  The second continuous measuring device 10 includes a second projection measuring device 11 and a second weak measuring device 12. The second projection measuring device 11 performs projection measurement based on the second PVM (hereinafter referred to as second projection measurement), that is, determination of whether the polarization state is | R> or | L>. Do.

The second weak measuring device 12 performs weak measurement with the second projection measurement as the final measurement . In the weak measurement, when the polarization state of a photon incident on the second continuous measuring device 10 belongs to the first PVM, the degenerate observable (hereinafter referred to as the first degenerate state) having the first PVM as a set of eigenstates. 1). In the present embodiment, the Pauli operator σ _Z is employed as the first observable.

  If the polarization state of a photon incident on the second continuous measuring instrument 10 belongs to the second PVM, the second projection measuring instrument 11 can correctly know the polarization state. The measurement result of the second weak measuring device 12 may not be used. Therefore, in that case, what kind of weak measurement the second weak measuring device 12 performs is arbitrary. As long as it is a weak measurement, the disturbance that the weak measurement act gives to the polarization state of the photon to be measured is so small that it can be ignored.

  FIG. 2B is a conceptual diagram of data stored in the recipient computer 13. Each time the receiver side computer 13 performs a weak measurement and a projection measurement on the photon obtained from the photon emitter 4 by the first or second continuous measuring device 7 or 10, an identification for identifying the photon on the receiver side is performed. In association with the information, the weak measurement result and the projection measurement result are stored in its own memory.

  The identification information on the receiver side corresponds to the identification information on the sender side. Specifically, the time slot of each photon is synchronized between the sender and receiver. Therefore, the same photon can be identified by common identification information between both computers 5 and 13. The identification information is a label assigned to each photon.

  As described above, a sufficient number of photons (for example, 1,000 or more, preferably 10,000 or more) are transmitted from the photon emitter 4 to the first or second continuous measuring device 7 or 10, and the sender A sufficient number of data (see FIGS. 2A and 2B) is stored in the side computer 5 and the reception side computer 13, respectively.

  The subsequent flow will be described with reference to FIG.

  The sender-side computer 5 selects one polarization from the union {| H> <H |, | V> <V |, | R> <R |, | L> <L |} of the first and second PVMs. A state is selected (step S1). This selection method may be random or arbitrary, but is preferably random in terms of security against eavesdropping. The subject of selection may be a sender.

  Next, the sender computer 5 refers to the data stored in its own memory (see FIG. 2 (a)), and determines a plurality of photons (see FIG. 2A) sent to the receiver in the polarization state selected in step S1. For example, the identification information of these photons (hereinafter referred to as an identification information group) is extracted and notified to the receiver side computer 13 through the public channel 14 (step S2).

  When the recipient computer 13 is notified of the identification information group, the receiver computer 13 refers to the data stored in its own memory (see FIG. 2B), and the first and second projections corresponding to the identification information group. A statistical distribution of measurement results, specifically, a histogram is obtained (step S3).

  Next, the receiver-side computer 13 based on the obtained histogram, the polarization state selected by the sender-side computer 5 in step S1, that is, the common polarization state (used for extracting the identification information group on the sender side) ( Hereinafter, it is determined whether or not the common polarization state selected on the sender side can be estimated (step S4).

  Hereinafter, the case where the sender computer 5 selects the state | H> in step S1 and notifies the receiver computer 13 of the corresponding identification information group in step S2 will be described in detail. .

  FIG. 4 exemplifies a histogram that the receiver computer 13 obtains in step S3 in this case. The receiver computer 13 obtains at least one of the histograms shown in FIGS.

  FIG. 4A is a histogram of photons for which the first projection measurement has been performed. Since it is determined whether or not | H> or | V> for a photon sent in the state | H>, the frequency of obtaining a correct result | H> obtains an incorrect result | V>. Greater than frequency. When a histogram with such a bias is obtained, the receiver side can estimate that the common polarization state selected on the sender side is | H>. That is, YES can be determined in step S4.

  In general, there is a bias in the histogram of the projection measurement result of an event in which the PVM selected as the base of the projection measurement by the distributor 6 coincides with the PVM belonging to the common polarization state selected on the sender side. Therefore, according to the histogram, the common polarization state selected on the sender side can be correctly estimated in principle.

  FIG. 4A shows an ideally biased result. In the projection measurement result histogram, when U is the highest frequency and V is the next highest frequency, U / V However, if a bias such as 1.5 or more, preferably 2 or more is obtained, it is estimated that the quantum state having the highest frequency is the common quantum state selected on the transmitter side. Good.

FIG. 4B is a histogram of photons for which the second projection measurement has been performed. Since the photon transmitted in the state | H> is subjected to the projection measurement by the wrong basis, that is, whether it is | R> or | L>, the probability of obtaining either result is ½. And there is no bias in the measurement results. For this reason, only from the measurement result of FIG. 4B, the PVM selected as the basis of the projection measurement is incorrect, and therefore the common polarization state selected on the sender side is | H> or | Although it is understood that V> (∵ | <H | R> | ² = | <V | R> | ² = | <H | L> | ² = | <V | L> | ² = 1/2 ), I can't say anything about it. That is, NO is determined in step S4.

  In general, there is a bias in the histogram of the projection measurement results of events in which the PVM selected as the basis of the projection measurement by the distributor 6 does not match the PVM to which the common polarization state selected on the sender side belongs. Absent. For this reason, the histogram indicates that the PVM selected as the basis of the projection measurement was incorrect, and therefore whether the common polarization state selected on the sender side belongs to the first or second PVM. Can be specified, but in principle it cannot be estimated which polarization state in the correct PVM.

  Although FIG. 4B shows an ideally unbiased result, the i-th projection whose total frequency is more than 1/2 of the number of photons represented by the identification information group, preferably more than 3/5. In the measurement result histogram, when the highest frequency is U and the lowest frequency is V, if U / V is less than 1.5, for example, less than 1.2, it is selected by the sender. The common quantum state may be specified as belonging to the j-th PVM, and it may be determined that the quantum state in the j-th PVM cannot be estimated. Here, i is 1 or 2, j is 2 when i is 1, and 1 when i is 2.

  Since the distributor 6 selects the correct base with a probability of 50%, the receiver computer 13 usually obtains the histogram of FIG. 4A together with the histogram of FIG. 4B. In that case, it can be estimated that the common polarization state selected on the sender side is | H> from only the histogram of FIG.

  However, since the number of photons (number of events) specified by the identification information group is finite and the number is desired to be as small as possible from the viewpoint of safety against eavesdropping, it is distributed in virtually all the events specified by the identification information group. It is possible that the vessel 6 chooses the wrong basis. That is, there may be a case where the receiver side can substantially obtain only the histogram of FIG.

  Here, “substantially” means that the number of events for which the correct basis (in this case, the first PVM) is selected is not zero, but the number of events is too small, and it is also affected by noise and weak measurement reaction. Thus, since there is no clear frequency deviation between H and V as shown in FIG. 4 (a), this also includes the case where | H> or | V> is unclear.

  A histogram whose total frequency is, for example, less than 1/15, preferably less than 1/10 of the number of photons specified by the identification information group, even if it can be identified as the result of the projection measurement with the correct basis selected. It is preferable not to consider in the determination in step S4.

  Returning to FIG. 3, the description will be continued. If the receiver-side computer 13 can estimate the common polarization state selected on the sender side from the histogram of the projection measurement result, as in the case where the result of FIG. 4A is obtained (step S4; YES), the process returns to step S1 again as the estimation is completed, and the sender computer 5 is notified of the next identification information group (return).

On the other hand, the receiver-side computer 13 estimates the common polarization state selected on the sender side from the projection measurement result histogram, as in the case where only the result of FIG. When it is determined that it cannot be performed (step S4; NO), a weak value as an average value is obtained from the result of the weak measurement using the wrong base projection measurement as the final measurement (step S5).

  In the case of NO in step S4, the receiver side can identify whether the common polarization state selected on the transmitter side belongs to the first or second PVM. By obtaining the weak value, it is possible to narrow down which element of the specified PVM is the common polarization state selected on the transmitter side.

  Hereinafter, the point that the common polarization state selected on the transmitter side can be estimated based on the weak value will be described from a theoretical viewpoint.

In general, a weak measurement is described by the preparation of a certain initial state | i> of the quantum system and POVM {| f _m ><f _m |} (where m is an index for identifying the measurement result). This is an operation to acquire information related to the observable of the quantum system under the condition that only a negligible disturbance is given to the quantum system at an intermediate stage from the final measurement. The disturbance given to the quantum system is negligibly small, but sufficient information cannot be obtained from the quantum system in one weak measurement. However, if the same initial state preparation and final measurement can be repeated, the number of weak measurement result ensembles corresponding to the number of repetitions is obtained, and the ensembles are classified into sub-ensembles according to the final measurement results. The average value converges to a value (real part) called a weak value as the number of repetitions increases. In addition, such a weak measurement result is classified according to the final measurement result as post-selection. The state of the final measurement result, that is, the theoretical value of the weak value of the observable A selected after the final state | f _m > is given by the following equation.

In the present embodiment, the weak value of Equation (1) is used as a means for estimating the starting state | i>. That is, if a weak value can be calculated without specifically knowing the starting state | i>, | i> can be estimated from the known observable A and the final state | f _m >.

Even if the receiver does not know which polarization state is the common polarization state selected on the sender side as the starting state, the event with the same starting state can be identified by the notification of the identification information group. Therefore, the weak value can be calculated by selecting the result of the weak measurement according to the result of the projection measurement as the final measurement. Therefore, the starting state can be estimated from the weak value, the known observable σ _Z or σ _Y, and the final state | R>, | L>, | H>, or | V>.

For example, even if it is possible to specify that the starting state belongs to the first PVM as in the case where only the histogram of FIG. 4B is obtained, it is obvious whether it is | H> or | V>. Think of a situation that does not. The second projection measurement based on the second PVM (| R> or | L>) is performed, and the weak measurement of the observable σZ is performed by the second weak measuring device 12 using the second projection measurement as the final measurement . . The ensemble of the weak measurement result is classified into two subensembles depending on whether the final state is | R> or | L>. That is, select after the fact. Then, a weak value can be calculated as an average value in each sub-ensemble.

On the other hand, since it is known that the start state is | H> or | V>, the weak value of the observable σ _Z that is selected after the end state | R> for each case is obtained from the equation (1). The following theoretical values are given.

The receiver does not know whether the initial state is | H> or | V>, but if the calculated value of the weak value of the observable σ _Z that is selected after the final state | R> is close to 1, From the equation (2), it can be specified that the starting state is | H>. Further, if the calculated value of the weak value is close to −1, it can be specified from the equation (3) that the starting state is | V>.

Similarly, the theoretical value of the weak value of the observable σ _Z that is selected after the final state | L> is given by the following equation (1).

Also in this case, if the calculated value of the weak value of the observable σ _Z that has been selected in the final state | L> is close to 1, the receiver determines that the initial state is | H> from Equation (4). If the calculated value of the weak value is close to −1, the starting state can be specified as | V> from the equation (5).

  After all, from the formulas (3) to (5), whether the calculated value of the weak value is close to 1 regardless of whether the state of the second projection measurement result as the final state is | R> or | L>. It can be seen that the starting state can be specified depending on whether it is close to. This means that there is no need for post-selection. That is, the average value of the second weak measurement results may be obtained anyway without paying attention to the second projection measurement results. The average value is a weak value when no subsequent selection is made.

  A simple calculation shows that the theoretical value of the weak value without the post-selection is equivalent to the expected value for the starting state, as shown in the following equation.

  Therefore, the receiver calculates the result of the weak measurement accompanying the second projection measurement as the final measurement, that is, the average value of the measurement result of the second weak measuring device 12, and the value (when the post-selection is not performed) If it is close to 1, the starting state can be specified as | H> from Equation (6), and if it is close to −1, the starting state can be specified as | V> from Equation (7).

The case has been described above where the second projection measurement is selected on the receiver side even though the start state belongs to the first PVM. Similarly, even when the initial state belongs to the second PVM and the first projection measurement is selected on the receiver side, the theoretical value of the weak value of the observable σ _Y without the subsequent selection is This is equivalent to the expected value for the starting state as shown in the following equation.

  Therefore, the receiver calculates the result of the weak measurement accompanying the first projection measurement, that is, the average value of the measurement result of the first weak measuring device 9, and the value (weak value when the post-selection is not performed). Is close to 1, the starting state can be specified as | R> from Equation (8), and when it is close to −1, the starting state can be specified from | L>.

  Returning to FIG. 3, the description of the flow after step S5 is continued.

If the receiver-side computer 13 determines NO in step S4, it extracts a weak measurement result whose final measurement is a projection measurement on the wrong basis from all ensembles of weak measurement results corresponding to the identification information group. Then, the average value in the extracted subensemble is calculated (step S5). As described above, this average value corresponds to a weak value when no post-selection is performed.

  Next, the receiver side computer 13 determines whether or not the common polarization state selected on the sender side can be specified based on the calculated weak value (step S6).

  For example, even if only the histogram of FIG. 4B is obtained in step S3, if the weak value is close to 1, the common polarization state selected on the sender side from Equation (6) is | H>. If it is close to −1, it can be specified as | V> from Equation (7). That is, YES can be determined in step S6.

  Similarly, even if only the same histogram as in FIG. 4B is obtained for the basis {| H>, | V>} in step S3, the receiver-side computer 13 obtains a weak value in the case where no subsequent selection is performed. If it is calculated and if it is close to 1, the common polarization state selected on the sender side from the equation (8) can be specified as | R>, and if close to −1, it can be determined from the equation (9) as | It can be specified that L>. That is, YES can be determined in step S6.

  Specifically, for example, the weak value when the post-selection is not performed is W, one eigenvalue of an observable without degeneration that is weakly measured is M, and the other eigenvalue closest thereto is N (where N> M) ), Where δ = | N−M | / 10, if W <(M + N) / 2−δ, since W is close to M, the common quantum state selected on the sender side corresponds to the eigenvalue M. If W> (M + N) / 2 + δ, since W is close to N, it is determined that the common quantum state selected on the transmitter side is an eigenstate corresponding to the eigenvalue N. Good (step S6; YES). On the other hand, for any M and N, if (M + N) / 2−δ ≦ W ≦ (M + N) / 2 + δ, it may be determined that the common quantum state selected on the sender side cannot be estimated (step S6; NO). Note that δ is preferably | N−M | / 5.

  In the present specific example, if the weak value in the case of no subsequent selection is less than −0.2, the common polarization state selected on the sender side is specified as | V> (step S6; YES). If it exceeds 0.2, it is specified that | H> (step S6; YES), and if it is −0.2 or more and 0.2 or less, it is determined that it cannot be specified (step S6; NO).

  If the receiver-side computer 13 can identify the common polarization state selected on the sender side based on the weak value in the case where the post-selection is not performed (step S6; YES), the process returns to step S1 again as the completion of estimation. The sender computer 5 is notified of the next group of identification information (return).

When the common polarization state selected on the sender side can be specified (step S4; YES and step S6; YES), the number of elements of the union of the first and second PVMs, that is, four elements in this case, This means that 2-bit information is transmitted from the sender side to the receiver side in the sense that one could be specified. In general, if the quantum system is an N-level system, 1 + log ₂ N-bit information is transmitted for each notification of the identification information group.

  According to the present embodiment, when this information is transmitted, it is not necessary to check the PVM for each quantum system between the sender and the receiver, which is necessary for the BB84 protocol. The complexity of communication between the computers 5 and 13 is reduced. By returning to step S1 and notifying the next group of identification information (return), information of a desired number of bits, for example, key data can be shared between the sender and the receiver.

  On the other hand, if the receiver-side computer 13 cannot identify the common polarization state selected on the sender side based on the weak value in the case where no subsequent selection is made (step S6; NO), there is a possibility of wiretapping. Is transmitted to the sender computer 5 through the public channel 14 (step S7).

  This is because the photon passes through the quantum channel 3 when the start state cannot be estimated from the projection measurement result or the weak measurement result even though the start state is the same in the event represented by the identification information group. This is because a third party may have performed a POVM measurement or projection measurement on the photon for eavesdropping in the process. That is, if the polarization state at the time of reaching the sorter 6 varies from the initial state due to wiretapping measurement, both the projection measurement result and the weak measurement result are noisy, and the statistical distribution of the result is not biased. . That is, the clarity is reduced.

  According to the present embodiment, in this way, the receiver side also evaluates the possibility that the eavesdropping POVM measurement or the projection measurement has been performed from the statistical distribution and the weak value of the projection measurement result corresponding to the identification information group. be able to.

  As a countermeasure when notifying the sender that there is a possibility of eavesdropping in step S7, it is possible to return to step S1 again to notify the sender of another group of identification information (return). This flow itself may be canceled.

When the quantum measurement for eavesdropping is weak measurement, this cannot be detected on the receiver side, but the weak measurement is meaningful only in combination with the final measurement. According to the present embodiment, the receiver computer 13 Does not disclose whether the basis is the first PVM or the second PVM as well as the result of the projection measurement as the final measurement, so that an eavesdropper can obtain meaningful information from the weak measurement result in principle. I can't. For this reason, safety against eavesdropping can be ensured.

  Although the quantum communication method according to the embodiment has been described above, the present invention is not limited to this.

  For example, in the example of FIG. 3, if “YES” is determined in step S4, “return” is set immediately. However, a weak value obtained from the weak measurement result associated with the wrong projection measurement result may be obtained for confirmation. For example, even when the histograms of both FIGS. 4A and 4B are obtained and it can be estimated that the starting state is | H> only from FIG. 4A, the projection of FIG. You may obtain | require the weak value obtained from the weak measurement result accompanying a measurement result. As a result, if a weak value close to 1 is obtained, it is confirmed that the starting state is | H>.

  Further, in the case of YES in step S4 of FIG. 3, the weak value obtained from the weak measurement result accompanying the correct projection measurement result may be obtained for confirmation. In this case, if it is made to obtain a noisy weak value, specifically, the same weak value (ideally zero) as in the case of determining NO in step S6, the noisy weak value can be obtained. This confirms that the base selection of the associated projection measurement is correct.

In this sense, the i-th weak measurement device (where i is 1 or 2) is the i-th PVM when the polarization state of the photon incident on the i-th continuous measurement device belongs to the i-th PVM. It is preferable that a weak measurement is performed for an observable without degeneracy with a set of eigenstates as a set of eigenstates for all elements of the PVM. Note that, as an undamaged observable whose state is a set of eigenstates with respect to all elements of the first PVM (| H> or | V>), for example, a Pauli operator as a second observable In addition to σ _Y , σ _{X and the} like can also be mentioned. Further, as an undegenerate observable whose state is a set of eigenstates with respect to all elements of the second PVM (| R> or | L>), for example, a Pauli operator as the first observable In addition to σ _Z , σ _{X and the} like can also be mentioned.

  Further, when the flow of FIG. 3 is repeated a plurality of times, the sender computer 5 may select the same polarization state as the polarization state already selected in the previous step S1 in step S1 again. In this case, it is preferable for safety against eavesdropping that the identification information group notified by the sender-side computer 5 includes identification information that does not include the identification information group already notified of the same polarization state. This is because notification of identification information is performed through the public channel 14, and if the identification information group for the same polarization state is the same every time, the eavesdropper detects that at least the same information is transmitted. Because it is possible.

  If a group of identification information includes identification information that is not included in the group of identification information that has already been notified of the same polarization state, the receiver uses the certain group for the purpose of confirming the estimation of the polarization state for the group of identification information The weak measurement result and the projection measurement result corresponding to the identification information group are merged with the weak measurement result and the projection measurement result used for the estimation already completed, respectively, and obtained from the statistical distribution and the weak measurement result of the merged projection measurement result. It is preferable to determine the weak value to be obtained.

  In the example of FIG. 3, the polarization state is estimated on the receiver side every time the identification information group is notified. First, the notification of the identification information group from the transmitter side to the receiver side is repeatedly performed a plurality of times. Thereafter, estimation of the quantum state for each identification information group may be performed collectively on the receiver side.

  In addition, after the receiver side obtains data of a certain number of bits by a plurality of notifications of the identification information group from the sender side to the sender side, as in the case of BB84, from the receiver side to the sender side It is also possible to send a subset of the navel data and analyze the error rate on the sender side. If the error rate is, for example, 25% or less, eavesdropping is not performed, and the remaining data may be held as a secret key between the sender and the receiver. Further, error correction may be performed.

  FIG. 5 shows a configuration example of the first continuous measuring instrument 7 of FIG.

  First, a case where a photon whose polarization state belongs to the second PVM (| R> or | L>) enters will be described.

  Photons emitted from the photon emitter 4 of FIG. 1 are incident on the quarter-wave plate 91. The quarter-wave plate 91 converts the clockwise circular polarization state | R> into a linear polarization state in the + 45 ° direction (hereinafter referred to as | +>), and converts the counterclockwise circular polarization state | L> to −45. It is converted into a linearly polarized state in the direction of ° (hereinafter referred to as |->). Here, | +> and |-> can be expressed as an overlap state of | H> and | V>, respectively, and | +> ∝ | H> + | V>, |-> ∝ | H>-| V>. .

  A photon whose polarization state is | +> or | −> is incident on the polarization beam splitter 92. The polarization beam splitter 92 transmits the | H> component (probability wave) while maintaining the phase relationship between the | H> component and | V> component of the photon incident on itself, and | V> component (probability wave). ) Is reflected. The | H> component propagates through the first internal optical path a, and the | V> component propagates through the second internal optical path b.

  A first half-wave plate 93 is disposed on the first internal optical path a. The first half-wave plate 93 has its principal axis inclined by an angle θ from the horizontal direction, and rotates the polarization direction of the | H> component incident thereon by an angle 2θ.

  A second half-wave plate 94 is disposed on the second internal optical path b. The second half-wave plate 94 has its principal axis inclined by an angle −θ from the horizontal direction, and rotates the polarization direction of the | V> component incident thereon by an angle −2θ.

  A beam splitter 95 is disposed at a position where the first internal optical path a and the second internal optical path b intersect, and constitutes a Mach-Zehnder interferometer together with the polarizing beam splitter 92.

  If the polarization state of the component incident on the beam splitter 95 from the first internal optical path a is | X>, and the polarization state of the component incident on the beam splitter 95 from the second internal optical path b is | Y>, the first internal The polarization state of the photons emitted to the first outgoing optical path c that is extended by transmitting the optical path a through the beam splitter 95 is proportional to | X> − | Y>, and the second internal optical path b is changed to the beam splitter. The polarization state of the photon emitted to the second outgoing optical path d that is transmitted through 95 and is extended is proportional to | X> + | Y>.

  The first projection measuring device 8 includes a polarizing beam splitter 80 disposed on the second outgoing optical path d, a first photon detector 81 on which a photon transmitted through the polarizing beam splitter 80 is incident, and a polarizing beam splitter. A second photon detector 82 on which the photons reflected by 80 are incident, a polarization beam splitter 83 disposed on the first output optical path c, and a third photon on which the photons transmitted through the polarization beam splitter 83 are incident. A photon detector 84 and a fourth photon detector 85 on which the photons reflected by the polarization beam splitter 83 are incident are provided. As the photon detector, for example, an avalanche photodiode (APD), a photomultiplier tube (PMT), a superconducting single photon detector (SSPD), or the like can be used.

In the above description, θ representing the rotation angle of the half-wave plates 93 and 94 from the main axis represents the measurement strength for the observable σ _Y.

  When θ = 22.5 °, the measured intensity is the strongest. At this time, the polarization state of the component propagating through the internal optical paths a and b becomes | +> by the half-wave plates 93 and 94, respectively, and becomes indistinguishable, causing maximum interference. When the polarization state of a photon incident on the quarter-wave plate 91 is | R>, the component | +> propagating through the internal optical path a and the component | +> propagating through the internal optical path b are in phase, so both Photons in the state | +> are emitted only from the second outgoing optical path d intensifying each other, and no photons are emitted from the first outgoing optical path c where both cancel each other. Similarly, when the polarization state of a photon incident on the quarter-wave plate 91 is | L>, the component | +> propagating through the internal optical path a and the component | +> propagating through the internal optical path b are in opposite phases. Therefore, photons in the state | +> are emitted only from the first emission optical path c, and no photons are emitted from the second emission optical path d.

For this reason, if a photon is emitted from the first emission optical path c, it is surely found that the polarization state of the photon incident on the quarter-wave plate 91 is | L>, and the photon is emitted from the second emission optical path d. When it is emitted, it can be surely understood that the polarization state of the photon incident on the quarter-wave plate 91 is | R>. Such a measurement corresponds to a projection measurement. Note that determining | R> means that the measurement result of observable σ _Y is 1, and determining | L> means that the measurement result of observable σ _Y is −1 (σ _Y = | R><R |-| L><L |).

  However, when θ = 22.5 °, when the polarization state of the photon incident on the quarter-wave plate 91 belongs to the first PVM (| H> or | V>), the first projection measuring device 8 In this case, there is a problem that it is impossible to determine at all whether | H> or | V>.

  When θ = 0 °, the measured intensity becomes zero. At this time, the polarization states of the components propagating through the internal optical paths a and b can be distinguished from | H> and | V>, respectively, so that no interference occurs. At this time, although the above-described adverse effect is completely eliminated, no matter whether the polarization state of the photon incident on the quarter-wave plate 91 is | R> or | L>, the photon is emitted from the first emission optical path c. The probability of emission and the probability of emission of a photon from the second emission optical path d are equally 50%. Whether the polarization state of the photon incident on the quarter-wave plate 91 is | R> or | L>. No information can be obtained.

  By setting 0 ° <θ <22.5 °, weak measurement can be realized. At this time, even if the polarization state of the photon incident on the quarter-wave plate 91 is | R>, the probability that the photon is emitted from the first emission optical path c is not zero. However, when the polarization state of the photon incident on the quarter-wave plate 91 is | R>, the photon is emitted from the second emission optical path d rather than the probability that the photon is emitted from the first emission optical path c. Probability is higher.

  Even if the polarization state of the photon incident on the quarter-wave plate 91 is | L>, the probability that the photon is emitted from the second emission optical path d is not zero. However, when the polarization state of the photon incident on the quarter-wave plate 91 is | L>, the photon is emitted from the first emission optical path c rather than the probability that the photon is emitted from the second emission optical path d. Probability is higher.

  Thus, whether the polarization state of the photon incident on the quarter-wave plate 91 is | R> depending on whether the photon is emitted from the first emission optical path c or the second emission optical path d. If the polarization state of the photon incident on the quarter-wave plate 91 belongs to the first PVM (| H> or | V>) while leaving a certain probability that it can be correctly determined whether The trade-off measuring device 8 is able to suppress the adverse effect of not being able to correctly determine whether | H> or | V>.

  From the viewpoint of further achieving such a balance, θ is preferably 0 ° <θ ≦ 16.875 °, more preferably 5.625 ≦ θ ≦ 16.875 °. For example, θ can be 11.25 °.

When the polarization state of the photon incident on the quarter-wave plate 91 is | R> or | L>, the result of the weak measurement is whether the photon is emitted from the first outgoing optical path c or the second outgoing optical path It is given by whether it radiates | emits from d. When the photon is emitted from the first emission optical path c, it is determined that the polarization state of the photon incident on the quarter-wave plate 91 is | L>, and the weak measurement result of the observable σ _Y is recorded as -1. To do. When the photon is emitted from the second emission optical path d, it is determined that the polarization state of the photon incident on the quarter-wave plate 91 is | R>, and the weak measurement result of the observable σ _Y is recorded as 1. . These recordings are performed by the recipient computer 13 in FIG.

  However, the polarization state of the photon emitted from the first emission optical path c and the polarization state of the photon emitted from the second emission optical path d are | +> or | −>. The first projection measuring device 8 determines whether or not | H> or | V> with respect to the photons in the state of | +> or | −>. Alternatively, it is completely equivalent to determining whether | H> or | V> for a photon in a state of | L>. In either case, | H> is determined with a probability of 50%, | V> is determined with a probability of 50%, and whether the original polarization state is | +> or | −>, or | R>. I can't say anything about L>. For this reason, whether or not a quarter-wave plate that returns the base {| +>, |->} to {| R>, | L>} is arranged in each of the outgoing optical paths c and d. Is optional.

  Next, a case where a photon whose polarization state belongs to the first PVM (| H> or | V>) enters the quarter-wave plate 91 will be described.

  The quarter-wave plate 91 does not change the polarization state when the polarization state of a photon incident on itself is | H> or | V>.

The photons in the state | H> are transmitted through the polarization beam splitter 92, and the polarization direction is rotated by a minute angle 2θ (where 0 ° <θ <22.5 °) by the half-wave plate 93. The polarization state is expressed as | H + ε>. Then, photons in the state | H + ε> are emitted from the emission optical path c or d. Since the state | H + ε> is close to the original state | H>, the probability that the first projection measuring device 8 correctly determines that | H> is higher than the probability that it is erroneously determined that | V>. That is, | <H | H + ε> | ² ≈1 is larger than | <V | H + ε> | ² ≈0.

The photons in the state | V> are reflected by the polarization beam splitter 92, and the polarization direction is rotated by a minute angle −2θ (where 0 ° <θ <22.5 °) by the half-wave plate 94. The polarization state is expressed as | V−ε>. Then, photons in the state | V−ε> are emitted from the emission optical path c or d. Since the state | V−ε> is close to the original state | V>, the probability that the first projection measuring device 8 correctly determines that | V> is higher than the probability that it is erroneously determined that | H>. . That is, | <V | V−ε> | ² ≈1 is larger than | <H | V−ε> | ² ≈0.

  As described above, when the polarization state of the photon incident on the quarter-wave plate 91 belongs to the first PVM (| H> or | V>), the measurement result of the first projection measuring instrument 8 is accurate. That is secured.

  When the state of the photon incident on the quarter-wave plate 91 is | H>, the probability that the photon in the state | H + ε> is emitted from the first emission optical path c is also from the second emission optical path d. The probability of emission is also 50%. In addition, when the state of the photon incident on the quarter-wave plate 91 is | H>, the probability that the photon in the state | V−ε> is emitted from the first emission optical path c is also the second emission optical path. The probability of emission from d is also 50%.

  This means that the first weak measuring device 9 has the first PVM when the polarization state of the photon incident on the quarter-wave plate 91 belongs to the first PVM (| H> or | V>). This means that a weak measurement is performed for an observable without degeneracy with a set of eigenstates as a set of eigenstates. The weak measurement result in this case does not necessarily need to be used because it does not include any information on whether | H> or | V>.

  Hereinafter, the storage operation of the recipient computer 13 in FIG. 1 will be described.

  When a photon is detected by the first photon detector 81, the receiver computer 13 stores that the weak measurement result is 1 and the first projection measurement result is | H>. The weak measurement result is set to 1 in this case because it is understood that a photon has exited from the second exit optical path d.

  This weak measurement result is particularly meaningful when the state of photons incident on the quarter-wave plate 91 belongs to the second PVM (| R> or | L>). When the state of the incident photon belongs to the first PVM (| H> or | V>), the data is not necessarily used, but is stored as 1 for the time being.

  When a photon is detected by the second photon detector 82, the receiver-side computer 13 stores that the weak measurement result is 1 and the first projection measurement result is | V>. The weak measurement result is set to 1 in this case because it is understood that a photon has exited from the second exit optical path d.

  When a photon is detected by the third photon detector 81, the receiver computer 13 stores that the weak measurement result is -1 and the first projection measurement result is | H>. The weak measurement result is set to −1 because in this case, it can be understood that a photon is emitted from the first emission optical path c.

  When a photon is detected by the fourth photon detector 85, the receiver-side computer 13 stores that the weak measurement result is -1 and the first projection measurement result is | V>. The weak measurement result is set to −1 because in this case, it can be understood that a photon is emitted from the first emission optical path c.

  FIG. 6 shows a configuration example of the second continuous measuring instrument 10 of FIG.

  First, a case where a photon whose polarization state belongs to the first PVM (| H> or | V>) enters will be described.

  Photons emitted from the photon emitter 4 of FIG. 1 are incident on the half-wave plate 121. The half-wave plate 121 has its principal axis inclined at an angle of 22.5 ° from the horizontal direction, and converts | H> to | +> and | V> to |->.

  Photons in the state | +> or | −> are incident on the polarization beam splitter 122. The polarization beam splitter 122 transmits the | H> component (probability wave) while maintaining the phase relationship between the | H> component and | V> component of the photon incident thereon, and | V> component (probability wave). ) Is reflected. The | H> component propagates in the first internal optical path e, and the | V> component propagates in the second internal optical path f.

  A first half-wave plate 123 is disposed on the first internal optical path e. The first half-wave plate 123 has its principal axis inclined by an angle θ from the horizontal direction, and rotates the polarization direction of the | H> component incident on itself by an angle 2θ.

  A second half-wave plate 124 is disposed on the second internal optical path f. The second half-wave plate 124 has its principal axis inclined by an angle −θ from the horizontal direction, and rotates the polarization direction of the | V> component incident thereon by an angle −2θ.

  A beam splitter 125 is disposed at a position where the internal optical paths e and f intersect, and constitutes a Mach-Zehnder interferometer together with the polarizing beam splitter 122. If the polarization state of the component incident on the beam splitter 125 from the first internal optical path e is | X> and the polarization state of the component incident on the beam splitter 125 from the second internal optical path f is | Y>, the first internal The polarization state of the photons emitted to the first outgoing optical path g that is extended by transmitting the optical path e through the beam splitter 125 is proportional to | X> − | Y>, and the second internal optical path f is changed to the beam splitter. The polarization state of the photon emitted to the second outgoing optical path h that is transmitted through 125 and extended is proportional to | X> + | Y>.

  The second projection determiner 11 includes a quarter-wave plate 110, a half-wave plate 111, a polarizing beam splitter 112, and a photon transmitted through the polarizing beam splitter 112, which are disposed on the second outgoing optical path h. First photon detector 113 on which light is incident, second photon detector 114 on which photons reflected by the polarizing beam splitter 112 are incident, and a quarter-wave plate disposed on the first outgoing optical path g 115, a half-wave plate 116, a polarizing beam splitter 117, a third photon detector 118 on which a photon transmitted through the polarizing beam splitter 117 is incident, and a fourth photon on which a photon reflected by the polarizing beam splitter 119 is incident. Photon detector 119.

In the above, θ representing the rotation angle of the half-wave plates 123 and 124 from the main axis represents the measurement strength for the observable σ _Z.

  When θ = 22.5 °, the measured intensity is the strongest. At this time, the polarization state of the component propagating in the internal optical paths e and f becomes | +> by the half-wave plates 123 and 124, respectively, and becomes indistinguishable, thereby causing maximum interference. When the polarization state of a photon incident on the half-wave plate 121 is | H>, the component | +> propagating through the internal optical path a and the component | +> propagating through the internal optical path b are in phase. Photons in the state | +> are emitted only from the second outgoing optical path h intensifying each other, and no photons are emitted from the first outgoing optical path g where both cancel each other. Similarly, when the polarization state of a photon incident on the half-wave plate 121 is | V>, the component | +> propagating through the internal optical path e and the component | +> propagating through the internal optical path f are in opposite phases. Therefore, photons in the state | +> are emitted only from the first emission optical path g, and no photons are emitted from the second emission optical path h.

For this reason, if a photon is emitted from the first emission optical path g, the polarization state of the photon incident on the half-wave plate 121 can be surely determined as | V>, and the photon is emitted from the second emission optical path h. If the light is emitted, it can be surely understood that the polarization state of the photon incident on the half-wave plate 121 is | H>. Such a measurement corresponds to a projection measurement. Note that determining that | H> is that the measurement result of the observable σ _Z is 1, and determining that | V> is that the measurement result of the observable σ _Z is −1 (σ _Z = | H><H | − | V><V |).

  However, when θ = 22.5 °, when the polarization state of the photon incident on the half-wave plate 121 belongs to the second PVM (| R> or | L>), the second projection measuring instrument 11 In this case, there is a problem that it is impossible to determine at all whether | R> or | L>.

  When θ = 0 °, the measured intensity becomes zero. At this time, the polarization states of the components propagating through the internal optical paths e and f can be distinguished from | H> and | V>, respectively, so that no interference occurs. At this time, although the above-described adverse effect is completely eliminated, the photon is incident from the first outgoing optical path g regardless of whether the polarization state of the photon incident on the half-wave plate 121 is | H> or | V>. The probability of emission and the probability of emission of a photon from the second emission optical path h are both 50%. What is the polarization state of the photon incident on the half-wave plate 121? I can't get information.

  By setting 0 ° <θ <22.5 °, weak measurement can be realized. At this time, even if the polarization state of the photon incident on the half-wave plate 121 is | V>, the probability that the photon is emitted from the second emission optical path h is not zero. However, when the polarization state of the photon incident on the half-wave plate 121 is | V>, the photon is emitted from the first outgoing optical path g rather than the probability that the photon is emitted from the second outgoing optical path h. Probability is higher.

  Even if the polarization state of the photon incident on the half-wave plate 121 is | H>, the probability that the photon is emitted from the first emission optical path g is not zero. However, when the polarization state of the photon incident on the half-wave plate 121 is | H>, the photon is emitted from the second emission optical path h rather than the probability that the photon is emitted from the first emission optical path g. Probability is higher.

  Thus, whether the polarization state of the photon incident on the half-wave plate 121 is | H> depending on whether the photon is emitted from the first emission optical path g or the second emission optical path h | V> If the polarization state of the photon incident on the half-wave plate 121 belongs to the second PVM (| R> or | L>) while leaving a certain probability that it can be correctly determined whether or not The trade-off measuring device 11 is able to suppress the adverse effect of not being able to correctly determine whether | R> or | L>.

  From the viewpoint of further achieving such a balance, θ is preferably 0 ° <θ ≦ 16.875 °, more preferably 5.625 ≦ θ ≦ 16.875 °. For example, θ can be 11.25 °.

When the polarization state of the photon incident on the half-wave plate 121 is | H> or | V>, the result of the weak measurement is whether the photon is emitted from the first outgoing optical path g or the second outgoing optical path It is given by whether it radiates from h. When the photon is emitted from the first emission optical path g, it is determined that the polarization state of the photon incident on the half-wave plate 121 is | V>, and the weak measurement result of the observable σ _Z is determined to be -1. To do. When the photon is emitted from the second emission optical path h, it is determined that the polarization state of the photon incident on the half-wave plate 121 is | H>, and the weak measurement result of the observable σ _Z is determined to be 1. .

  However, the polarization state of the photon emitted from the first emission optical path g and the polarization state of the photon emitted from the second emission optical path h are | +> or | −>. The second projection measuring device 11 determines whether or not | R> or | L> with respect to the photons in the | +> or |-> state. Alternatively, it is completely equivalent to determining whether or not | R> or | L> for a photon in a state of | V>. In either case, it is determined as | R> with a probability of 50%, and determined as | L> with a probability of 50%, and whether the original polarization state is | +> or | −> or | H>. I can't say anything about V>. For these reasons, it is optional whether an optical element for returning the base {| +>, |->} to {| H>, | V>} is arranged in each of the outgoing optical paths h and g. It is.

  Next, a case where a photon whose polarization state belongs to the second PVM (| R> or | L>) enters the half-wave plate 121 will be described.

  The half-wave plate 121 converts | R> to | L> and converts | L> to | R>.

  Photons in the state | R> or | L> are incident on the polarization beam splitter 122. The polarization beam splitter 122 transmits the | H> component (probability wave) while maintaining the phase relationship between the | H> component and | V> component of the photon incident thereon, and | V> component (probability wave). ) Is reflected. The | H> component propagates in the first internal optical path e, and the | V> component propagates in the second internal optical path f.

  The first half-wave plate 123 rotates the polarization direction of the | H> component by a minute angle 2θ (where 0 ° <θ <22.5 °). The polarization state is expressed as | H + ε>.

  The second half-wave plate 124 rotates the polarization direction of the | V> component by a minute angle −2θ (where 0 ° <θ <22.5 °). The polarization state is expressed as | V−ε>.

  When the polarization state of a photon incident on the half-wave plate 121 is | R>, a photon in a state of | H + ε> −i | V−ε> is emitted from the second output optical path h with a probability of 50%. Then, photons in a state of | H + ε> + i | V−ε> are emitted from the first outgoing light path g with a probability of the remaining 50% (however, the normalization constant of the state is omitted here for simplicity).

  Since the state of | H + ε> −i | V−ε> is a counterclockwise elliptical polarization state close to the counterclockwise circular polarization state | L>, a photon in the state | L> has a second emission optical path h for simplicity. A case where the light enters the second projection measuring device 11 will be described. The quarter-wave plate 110 converts | L> to |->, and the half-wave plate 111 converts |-> to | V>. In addition, the quarter wavelength plate 110 and the half wavelength plate 111 may be combined with one quarter wavelength plate having a declination angle of 45 °.

  Photons in the state | V> are reflected by the polarization beam splitter 112 and enter the second photon detector 114. Thus, when a photon is detected by the second photon detector 114, it can be estimated that the polarization state of the photon incident on the half-wave plate 121 is | R>.

  Since the state | H + ε> + i | V−ε> is a clockwise elliptical polarization state close to the clockwise circular polarization state | R>, the photons in the state | R> are removed from the first outgoing optical path g for simplicity. A case where the light enters the second projection measuring device 11 will be described. The quarter-wave plate 115 converts | R> to | +>, and the half-wave plate 116 converts | +> to | H>. The quarter wavelength plate 115 and the half wavelength plate 116 can also serve as one quarter wavelength plate having a declination angle of 45 °.

  Photons in the state | H> pass through the polarization beam splitter 117 and enter the third photon detector 118. Thus, when a photon is detected by the third photon detector 118, it can be estimated that the polarization state of the photon incident on the half-wave plate 121 is | R>.

  When the polarization state of a photon incident on the half-wave plate 121 is | L>, a photon in a state of | H + ε> + i | V−ε> is emitted from the second output optical path h with a probability of 50%. A photon in a state of | H + ε> −i | V−ε> is emitted from the first outgoing light path g with a probability of the remaining 50% (however, the normalization constant of the state is omitted here for simplicity).

  Since the state | H + ε> + i | V−ε> is close to | R>, a case where a photon in the state | R> is incident on the second projecting measuring instrument 11 from the second outgoing optical path h will be described. To do. The quarter-wave plate 110 converts | R> to | +>, and the half-wave plate 111 converts | +> to | H>. The photons in the state | H> pass through the polarization beam splitter 112 and enter the first photon detector 113. Thus, when a photon is detected by the first photon detector 113, it can be estimated that the polarization state of the photon incident on the half-wave plate 121 is | L>.

  Since the state | H + ε> −i | V−ε> is close to | L>, the photon in the state | L> is incident on the second projecting measuring instrument 11 from the first outgoing optical path g for simplicity. explain. The quarter-wave plate 115 converts | L> to |->, and the half-wave plate 116 converts |-> to | V>. Photons in the state | V> are reflected by the polarization beam splitter 117 and enter the fourth photon detector 119. Thus, when a photon is detected by the fourth photon detector 119, it can be estimated that the polarization state of the photon incident on the half-wave plate 121 is | L>.

The second projection measuring instrument 11 may determine the state | H + ε> −i | V−ε> as | R>, but the probability of determining this as | L> is higher. . That is, | <L | (| H + ε> −i | V−ε>) | ² ≈1 is larger than | <R | (| H + ε> −i | V−ε>) | ² ≈0. Further, the second projection measuring instrument 11 may determine the state | H + ε> + i | V−ε> as | L>, but the probability of determining this as | R> is higher. That is, | <R | (| H + ε> + i | V−ε>) | ² ≈1 is larger than | <L | (| H + ε> + i | V−ε>) | ² ≈0.

  Therefore, when the polarization state of the photon incident on the half-wave plate 121 belongs to the second PVM (| R> or | L>), the accuracy of the measurement result in the second projection measuring instrument 11 is guaranteed. Is done.

  When the state of the photon incident on the half-wave plate 121 is | R>, both the probability that the photon is emitted from the first emission optical path g and the probability that the photon is emitted from the second emission optical path h are 50. %. Even when the state of the photon incident on the half-wave plate 121 is | L>, both the probability that the photon is emitted from the first emission optical path g and the probability that the photon is emitted from the second emission optical path h are 50%. It is.

  This means that the second weak measuring device 12 uses the second PVM when the polarization state of the photon incident on the half-wave plate 121 belongs to the second PVM (| R> or | L>). This means that a weak measurement is performed for an observable without degeneracy with a set of eigenstates as a set of eigenstates. The weak measurement result in this case does not necessarily need to be used because it does not include any information about whether | R> or | L>.

  Hereinafter, the storage operation of the recipient computer 13 in FIG. 1 will be described.

  When a photon is detected by the first photon detector 113, the receiver computer 13 stores that the weak measurement result is 1 and the second projection measurement result is | L>. The weak measurement result is set to 1 in this case because it is understood that a photon has exited from the second exit optical path h.

  This weak measurement result is particularly meaningful when the polarization state of a photon incident on the half-wave plate 121 belongs to the first PVM (| H> or | V>). If the polarization state of the photon incident on the light beam belongs to the second PVM (| R> or | L>), the data is not necessarily used, but is stored as 1 for the time being.

  When the second photon detector 114 detects a photon, the receiver computer 13 stores that the weak measurement result is 1 and the second projection measurement result is | R>. The weak measurement result is set to 1 in this case because it is understood that a photon has exited from the second exit optical path h.

  When photons are detected by the third photon detector 118, the receiver computer 13 stores that the weak measurement result is -1 and the second projection measurement result is | R>. The weak measurement result is set to −1 because in this case, it is understood that a photon is emitted from the first emission optical path g.

  When a photon is detected by the fourth photon detector 119, the receiver-side computer 13 stores that the weak measurement result is -1 and the second projection measurement result is | L>. The weak measurement result is set to −1 because in this case, it is understood that a photon is emitted from the first emission optical path g.

  5 and 6 are only a specific example. Generally, as each of the first and second continuous measuring devices, for each of a photon incident from the first outgoing optical path (c; g) and a photon incident from the second outgoing optical path (d; h) Then, the projection measuring device (8; 11) that performs the projection measurement based on the final measurement PVM, and the first optical path (a; e) of the photon incident on itself by the orthogonal linearly polarized light component. After branching to the second internal optical path (b; f), the interferometer that demarcates the first and second outgoing optical paths by overlapping again, and the first and second internal optical paths A polarization rotator (93, 94; 123, 24) for rotating the polarization direction of the component propagating in at least one of the first and second internal optical paths so that the polarization direction of the propagating component approaches each other. Quantum measuring instruments can be used. Examples of the interferometer include not only a Mach-Zehnder interferometer but also a Sagnac interferometer. It is a matter of design for those skilled in the art how to implement such a quantum measuring device depending on the first and second PVM used.

  As mentioned above, although this invention was demonstrated along embodiment, this invention is not limited to this.

  In the above embodiment, an example of polarization encoding that puts information on the polarization state of a photon has been shown. However, a state in which a photon exists at a first time position and a second time position after the first time position. It is also possible to use a phase encoding in which information is put on the phase difference between these two components using a superposition state with a state existing in.

  In addition, the quantum system serving as a medium for carrying information is not limited to photons, but may be electrons or other elementary particles, natural or artificial atoms, molecules, superconductors, or other macroscopic systems. It will be apparent to those skilled in the art that various modifications, improvements, combinations, and the like can be made.

  Hereinafter, preferred embodiments of the present invention extracted from the description of the present specification will be added.

(Appendix 1)
Whether the step (d) is (d1) the receiving device can estimate the same quantum state from the statistical distribution of the projection measurement result in the step (b) for each quantum system corresponding to the identification information group. And (d2) the weak measurement result in step (b) for each quantum system corresponding to the identification information group when it is determined that the same quantum state cannot be estimated. Are classified according to which of the first and second projection measurements is performed, an average value in the classified sub-ensemble is obtained as the weak value, and the same quantum state is estimated based on the average value. A quantum communication method including a process.

(Appendix 2)
When the step (d2) (d3) determines whether the receiving apparatus can estimate the same quantum state from the weak value, and (d4) determines that the receiving apparatus cannot estimate, the receiving apparatus The quantum communication method according to appendix 1, including a step of notifying the transmitting apparatus that there is a possibility of

(Appendix 3)
In the step (c), the identification information group for specifying a plurality of quantum systems transmitted in a certain quantum state includes identification information that does not include the identification information group already notified of the same quantum state. A quantum communication method that repeatedly notifies information groups.

(Appendix 4)
Projection obtained by merging the weak measurement result and the projection measurement result corresponding to one identification information group with the weak measurement result and the projection measurement result corresponding to another identification information group in the step (d). The quantum communication method according to appendix 3, including a step of obtaining a weak distribution obtained from a statistical distribution of measurement results and a weak measurement result.

(Appendix 5)
Each of the first and second continuous measuring devices projects a photon incident from the first outgoing optical path and a photon incident from the second outgoing optical path based on the final measurement PVM. The first and second projection measuring instruments that perform the measurement and the optical paths of the photons incident on the self are split into a first internal optical path and a second internal optical path by orthogonal polarization components, and then overlapped again. Two interferometers that define two outgoing optical paths and at least one of the first and second internal optical paths so that the polarization directions of the components propagating through the first and second internal optical paths are close to each other A quantum communication system comprising a polarization rotator that rotates a polarization direction of a component to be rotated.

(Appendix 6)
When a photon in a polarization state belonging to a weak measurement PVM made of a non-orthogonal element with respect to the final measurement PVM is incident on the interferometer, the emission probability from the first emission optical path according to the polarization state 6. The quantum communication according to appendix 5, wherein the photon in a polarization state that does not cause a bias in the projection measurement result is emitted from any of the outgoing light paths under a condition in which a bias occurs in the emission probability from the second outgoing light path. system.

(Appendix 7)
Supplementary Note 5: When a photon in a polarization state belonging to the final measurement PVM is incident, the photon in a polarization state that causes a bias in the projection measurement result is emitted from one of the first and second emission optical paths. Or a quantum communication system according to 6;

(Appendix 8)
The probability of emission of the photon from the first output optical path is equal to the probability of output of the photon from the second output optical path when a polarized photon belonging to the final measurement PVM is incident. The quantum communication system according to appendix 7.

  The quantum communication technique of the present invention can be used, for example, for quantum key distribution that shares key data necessary for encryption. For example, secure encryption communication can be realized by using data shared using the quantum communication technology of the present invention as a key of a one-time pad.

  DESCRIPTION OF SYMBOLS 1,20 ... Transmitter, 2, 21 ... Receiver, 3, 22 ... Quantum channel, 4, 24 ... Photon emitter (quantum emitter), 5, 25 ... Sender computer, 6, 26 ... Sorter , 7 ... 1st continuous measuring device, 8, 27 ... 1st projection measuring device, 9 ... 1st weak measuring device, 10 ... 2nd continuous measuring device, 11, 28 ... 2nd projection measuring device, DESCRIPTION OF SYMBOLS 12 ... 2nd weak measuring device, 13, 29 ... Receiver computer, 14, 23 ... Public channel, 80, 83 ... Polarizing beam splitter, 81, 82, 84, 85 ... Photon detector, 91 ... 1/4 Wave plate, 92... Polarizing beam splitter, 93, 94... Half wave plate (polarization rotator), 95... Beam splitter, 110, 115. , 117... Polarization beam splitter, 113, 114, 11 , 119 ... Photon detector, 121 ... 1/2 wavelength plate, 122 ... Polarization beam splitter, 123, 124 ... 1/2 wavelength plate (polarization rotator), 125 ... Beam splitter, a, e ... First internal optical path , B, f ... second internal optical path, c, g ... first outgoing optical path, d, h ... second outgoing optical path.

Claims (3)

(A) An element selected at random from a union of a first PVM determined in advance between a sender and a receiver and a second PVM composed of elements that are non-orthogonal to the elements of the first PVM. Sending a quantum system prepared for the quantum state to be represented to the receiver one after another;
(B) For each of the quantum systems acquired from the transmission device by the reception device, a first projection measurement based on the first PVM and a first weak measurement based on the first projection measurement; and A step of randomly selecting any one of the continuous measurement of the second projection measurement based on the second PVM and the second weak measurement based on the second projection measurement, wherein the first weak measurement includes: When the quantum state of the quantum system acquired from the transmission device belongs to the second PVM, the second weak measurement is performed for the non-degenerate observable with the second PVM as a set of eigenstates. When a quantum state of a quantum system acquired from a device belongs to the first PVM, a process performed for a non-degenerate observable having the first PVM as a set of eigenstates;
(C) a step of notifying the receiving device of an identification information group for specifying a plurality of the quantum systems sent in the same quantum state among the quantum systems sent in the step (a);
(D) The receiving device obtains a weak value obtained from the statistical distribution of the projection measurement result and the weak measurement result in the step (b) for each quantum system corresponding to the identification information group, and obtains the statistical distribution and the weak quantum communication method including the step that identifies the same quantum state using the value. The first projection measurement based on the first PVM and the first weak measurement based on the first projection measurement are performed on the quantum system incident on the self, and the first weak measurement is incident on the self. When the quantum state of the quantum system belongs to the second PVM composed of elements that are non-orthogonal to the elements of the first PVM, the degenerate observable with the second PVM as a set of eigenstates is performed. A first continuous measuring instrument configured as follows:
A second projection measurement based on the second PVM and a second weak measurement using the second projection measurement as a final measurement are performed on the quantum system incident on the self, and the second weak measurement is incident on the self. A second continuous measuring device configured to be performed on an undegenerate observable having the first PVM as a set of eigenstates when the quantum state of the quantum system belongs to the first PVM;
A sorter that randomly enters each of the quantum systems acquired one after another from the outside to either the first continuous measuring device or the second continuous measuring device;
The identification information identifying each quantum system acquired by the distributor, the ability to the first or second continuous instrument measurement results association with each other about the quantum system, and acquired by the distributor The identification information group for specifying a plurality of acquired quantum systems in the same quantum state is acquired from the outside, and the first and second continuous measurements for each quantum system corresponding to the acquired identification information group seeking Yowachi obtained from the statistical distribution and weak measurements of projection measurements at vessels, using statistical distributions and Yowachi asked a recipient's computer having a function to identify the same quantum state Quantum communication receiver. The quantum system is represented in a quantum state represented by an element selected at random from a union of a first PVM determined in advance between a sender and a receiver and a second PVM consisting of non-orthogonal elements. A quantum-based emitter that prepares and emits one after another;
A sender-side computer that stores identification information for identifying each quantum system emitted from the quantum-system emitter in association with a quantum state of the quantum system prepared by the quantum-system emitter;
A first projection measurement based on the first PVM and a first weak measurement based on the first projection measurement are performed on the quantum system incident on the self, and the first weak measurement is incident on the self. A first continuous measuring device configured to be performed on an undegenerate observable having the second PVM as a set of eigenstates when the quantum state of the quantum system belongs to the second PVM;
A second projection measurement based on the second PVM and a second weak measurement using the second projection measurement as a final measurement are performed on the quantum system incident on the self, and the second weak measurement is incident on the self. A second continuous measuring device configured to be performed on an undegenerate observable having the first PVM as a set of eigenstates when the quantum state of the quantum system belongs to the first PVM;
A sorter that causes each quantum system emitted from the quantum system emitter to randomly enter one of the first continuous measurement device and the second continuous measurement device,
A receiver-side computer communicably connected to the sender-side computer, each quantum system emitted from the quantum-system emitter on the receiver side in correspondence with the identification information in the sender-side computer The identification information for identifying the quantum system and the function of storing the measurement result of the first or second continuous measurement device in association with the quantum system, as well as emitted from the quantum system emitter from the sender computer When a plurality of identification information groups specifying a plurality of quantum systems emitted in the same quantum state are transmitted, the first and second continuous measuring devices for each quantum system corresponding to the identification information group recipient computer to determine the Yowachi obtained from the statistical distribution and weak measurements of projection measurements, has the ability to identify the same quantum state using the statistical distribution and Yowachi determined in Quantum communication systems with and.