Processing device, quantum communication system, processing method, and program

Abstract

Provided are: a processing device capable of evaluating polarization dependency of visibility of a Mach-Zehnder interferometer; a quantum communication system; a processing method; and a program. According to the present invention, in two orthogonal polarization modes of input light beams, a polarization mode phase mismatch amount calculation means calculates a polarization mode phase mismatch amount representing a difference in phase conditions between light in two polarization modes when the light beam in each polarization mode propagates through two arms, which have an optical path length difference of the Mach-Zehnder interferometer, and interfere with a multiplexer / demultiplexer. A light intensity mismatch amount calculation means calculates a light intensity mismatch amount between the two input pulse light beams when the input pulse light beams propagating through the two arms of the Mach-Zehnder interferometer interfere with the multiplexer / demultiplexer. A visibility calculation means calculates the dependence of the visibility of the Mach-Zehnder interferometer on the polarization state of the input light beams on the basis of the polarization mode phase mismatch amount and the light intensity mismatch amount.

Description

Processing device, quantum communication system, processing method and program

[0001] The present disclosure relates to a processing device, a quantum communication system, a processing method, and a program.

[0002] In order to improve the confidentiality of communications, the use of a communication system that applies a quantum key distribution (QKD) method has been considered, as in Patent Document 1. In QKD, suppression of the quantum bit error rate (QBER) is important in order to ensure communication quality.

[0003] In a phase-coding QKD system using a Mach-Zehnder (MZ) interferometer, the main factor in QBER is the visibility of the MZ interferometer. Generally, birefringence occurs in the medium that constitutes the optical waveguide, and the visibility varies depending on the state of polarization (SOP) of the light input to the MZ interferometer. As a result, variations in QBER occur due to the SOP.

[0004] JP 2016-10161 A

[0005] Therefore, to estimate the fluctuation in QBER, it is necessary to understand the fluctuation in the visibility of the MZ interferometer. However, there is no method to calculate the visibility taking into account the polarization dependency of the MZ interferometer, i.e., birefringence. Therefore, it has been difficult to physically understand the effect that the polarization dependency of the MZ interferometer has on the visibility.

[0006] The processing device according to the present disclosure comprises: a phase mismatch amount calculation means for calculating a polarization mode phase mismatch amount representing the difference in phase conditions between light of two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of a Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; a light intensity mismatch amount calculation means for calculating a light intensity mismatch amount between two input pulse lights when input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and a visibility calculation means for calculating the dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the input light based on the phase mismatch amount and the light intensity mismatch amount.

[0007] The quantum communication system according to the present disclosure comprises: a transmitting device that transmits a quantum signal consisting of a double optical pulse based on the BB84 protocol; a receiving device that outputs a detection signal obtained by decoding the quantum signal using a Mach-Zehnder interferometer; and a processing device that calculates, based on the detection signal, the dependency of the visibility of the Mach-Zehnder interferometer on the polarization of the quantum signal; a phase mismatch amount calculating means that calculates, in two orthogonal polarization modes of input light, a polarization mode phase mismatch amount that represents a difference in phase condition between light of each polarization mode when the light of the two polarization modes propagates through two arms of the Mach-Zehnder interferometer having an optical path length difference and interferes at an optical multiplexer / demultiplexer; an optical intensity mismatch amount calculating means that calculates an optical intensity mismatch amount between the two input pulse lights when the input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the optical multiplexer / demultiplexer; and a visibility calculating means that calculates, based on the phase mismatch amount and the optical intensity mismatch amount, the dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the quantum signal.

[0008] The processing method according to the present disclosure calculates a polarization mode phase mismatch amount representing a difference in phase condition between light of two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of a Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; calculates an optical intensity mismatch amount between two input pulse lights when input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and calculates the dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the input light based on the phase mismatch amount and the optical intensity mismatch amount.

[0009] The program according to the present disclosure causes a computer to execute the following processes: calculating a polarization mode phase mismatch amount representing a difference in phase condition between light of two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of a Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; calculating an optical intensity mismatch amount between two input pulse lights when input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and calculating the dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the input light based on the phase mismatch amount and the optical intensity mismatch amount.

[0010] According to the present disclosure, it is possible to provide a processing device, a quantum communication system, a processing method, and a program that are capable of evaluating the polarization dependency of the visibility of a Mach-Zehnder interferometer.

[0011] FIG. 1 is a block diagram schematically showing a configuration of a quantum communication system according to an embodiment. FIG. 1 is a diagram schematically showing a configuration of a receiving device according to an embodiment. FIG. 2 is a diagram showing light propagation in a Mach-Zehnder interferometer. FIG. 2 is a block diagram schematically showing a configuration of a processing device according to an embodiment. FIG. 3 is a block diagram schematically showing a configuration of a processing device according to an embodiment. FIG. 4 is a flowchart of a visibility calculation operation in a processing device according to an embodiment. FIG. 5 is a diagram showing a relationship between a resonant frequency interval and a polarization dependent frequency shift. FIG. 3 is a block diagram schematically showing a configuration of a processing device according to an embodiment. FIG. 4 is a flowchart of a visibility calculation operation in a processing device according to an embodiment. FIG. 5 is a block diagram schematically showing a configuration of a processing device according to an embodiment. FIG. 6 is a flowchart of an operation in a processing device according to an embodiment. FIG. 7 is a diagram showing a simulation of a probability density of a quantum bit error rate. FIG. 8 is a diagram showing an example configuration of a computer for realizing a processing device.

[0012] Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the drawings, the same elements are designated by the same reference numerals, and redundant explanations will be omitted as necessary.

[0013] When referring to one embodiment below, it means that the present invention can be applied to any one of the embodiments described below or a combination of two or more embodiments, and is not limited to a specific embodiment.

[0014] A quantum communication system according to a first embodiment will be described. The quantum communication system is configured to perform quantum key distribution using the BB84 protocol. Fig. 1 is a block diagram showing a schematic configuration of a quantum communication system according to one embodiment. The quantum communication system 1000 includes a transmitting device 100, a receiving device 200, and transmission paths 300 and 400.

[0015] The transmitting device 100 transmits a quantum signal or other signals (e.g., a synchronization signal) to the receiving device 200 via a transmission path 300 configured as a secret communication path. Furthermore, the transmitting device 100 and the receiving device 200 can transmit and receive signals including, for example, basis information, test bits, error correction information, etc. via a transmission path 400 that is a public communication path.

[0016] In this embodiment, the transmitting device 100 applies the BB84 protocol to transmit a double optical pulse DLP, which is a quantum signal consisting of a front pulse PL1 and a rear pulse PL2, to the receiving device 200. Hereinafter, the delay amount of the rear pulse PL2 relative to the front pulse PL1 is defined as Δt. Various configurations capable of transmitting the double optical pulse DLP can be applied to the transmitting device 100.

[0017] Next, the transmission and reception of quantum signals in this embodiment will be described. First, the operation of the transmitting device 100 will be described. The front pulse PL1 and the rear pulse PL2 included in the doublet optical pulse are individually phase-modulated before being output from the transmitting device 100. In this configuration, for example, the doublet optical pulse is branched into two, and a phase modulator is provided on each of the two branched paths. One phase modulator then imparts a phase shift of 0 or π / 2 (φ1 = {0, π / 2}) to the optical pulse. The other phase modulator also imparts a phase shift of 0 or π (φ2 = {0, π}). By combining the two doublet optical pulses after the phase shifts, four non-orthogonal states required by the BB84 protocol are generated.

[0018] In the first state, the front pulse PL1 is phase-modulated by {φ1,φ2}={0,0}, and the rear pulse PL2 is phase-modulated by {φ1,φ2}={0,π}. In this case, when the two phase-modulated doublet optical pulses are combined, only the front pulse PL1 with an intensity of 1 exists.

[0019] The second state is a case where the same phase modulation as in the first state is performed in the reverse order, that is, the phase modulation of {φ1,φ2}={0,π} is performed on the front pulse PL1 and the phase modulation of {φ1,φ2}={0,0} is performed on the rear pulse PL2. In this case, when the two phase-modulated doublet optical pulses are combined, only the rear pulse PL2 with an intensity of 1 exists.

[0020] Here, the first and second states are considered to be "two states belonging to the Z basis," and the first state is assigned a bit "0," and the second state is assigned a bit "1." Because the first and second states are orthogonal, they can be easily distinguished by measurement.

[0021] The third state is a case where the front pulse PL1 of the doublet optical pulse is phase-modulated by {φ1, φ2}={π / 2, 0} and the rear pulse PL2 is phase-modulated by {φ1, φ2}={π / 2, π}. In this case, when the two phase-modulated doublet optical pulses are combined, a state is created in which a doublet optical pulse is present, consisting of the front pulse PL1 having an intensity of 1 / 2 and a phase of π / 4 and the rear pulse PL2 having an intensity of 1 / 2 and a phase of −π / 4.

[0022] The fourth state is a case where the same phase modulation as in the third state is performed in the reverse order, that is, the front pulse PL1 of the doublet optical pulse is phase-modulated by {φ1,φ2}={π / 2,π}, and the back pulse PL2 is phase-modulated by {φ1,φ2}={π / 2,0}. In this case, when the two phase-modulated doublet optical pulses are combined, a doublet optical pulse is present, which consists of the front pulse PL1 with an intensity of 1 / 2 and a phase of -π / 4, and the back pulse PL2 with an intensity of 1 / 2 and a phase of π / 4.

[0023] Here, the third and fourth states are considered to be "two states belonging to the Y basis," and the third state is assigned a bit "0," and the fourth state is assigned a bit "1." Because the third and fourth states are orthogonal, they can be easily distinguished by measurement.

[0024] As described above, the four non-orthogonal states required by the BB84 protocol can be realized by using two phase modulators connected in parallel with two optical pulses.

[0025] Next, the configuration of the receiving device 200 will be described. Fig. 2 is a diagram schematically illustrating the configuration of the receiving device according to one embodiment. The receiving device 200 includes an optical coupler 1, a Mach-Zehnder (MZ) interferometer 2, an optical coupler 3, a signal processing unit 4, optical waveguides WG1 to WG6, and single-photon detectors PD1 to PD4. Note that, for example, avalanche photodiodes (APDs) are used as the single-photon detectors.

[0026] The optical coupler 1 is a two-input, two-output optical coupler that branches the double optical pulse DLP output from the transmitting device 100, for example, at the same intensity ratio, into an optical waveguide WG5 connected to the MZ interferometer 2 and an optical waveguide WG6 connected to the optical coupler 3.

[0027] The MZ interferometer 2 is configured as a decoding unit that decodes quantum signals using an asymmetric Mach-Zehnder interferometer. The MZ interferometer 2 has arms A1 and A2 and multiplexers / demultiplexers M1 and M2.

[0028] In the following description of the MZ interferometer 2, for simplicity, it is assumed that two successive optical pulses in the third and fourth states, which are the Y basis, are input to the receiving device 200.

[0029] The multiplexer / demultiplexer M1 branches the doublet optical pulse DLP input via the optical waveguide WG5 into two arms A1 and A2 of the Mach-Zehnder interferometer. The optical path length of the arm A1 is L, while the optical path length of the arm A2 is L+ΔL, which is longer than that of the arm A1. Here, the optical pulse propagating through the arm A2 is delayed by Δt relative to the optical pulse propagating through the arm A1 due to the optical path length difference ΔL.

[0030] The multiplexer / demultiplexer M2 multiplexes a double optical pulse DLP input via arm A1 and a double optical pulse DLP input via arm A2. Because there is an optical path length difference between arms A1 and A2 that delays the optical pulse by Δt, a triplet optical pulse TLP is generated by the two double optical pulses multiplexed by the multiplexer / demultiplexer M2. In this triplet optical pulse TLP, the front pulse PL1 that has passed through arm A1 becomes the leading pulse. The rear pulse PL2 that has passed through arm A2 becomes the last pulse. The rear pulse PL2 that has passed through arm A1 and the front pulse PL1 that has passed through arm A2 and has been given a delay Δt interfere with each other, forming a central pulse between the leading pulse and the last pulse.

[0031] When the post-pulse PL2 that has passed through arm A1 and the pre-pulse PL1 that has passed through arm A2 and been given a delay Δt are multiplexed in opposite phases, the multiplexer / demultiplexer M2 outputs a triplet optical pulse TLP to the optical waveguide WG1 that is connected to the single-photon detector PD1. When the post-pulse PL2 that has passed through arm A1 and the pre-pulse PL1 that has passed through arm A2 and been given a delay Δt are multiplexed in phase, the multiplexer / demultiplexer M2 outputs a triplet optical pulse TLP to the optical waveguide WG2 that is connected to the single-photon detector PD2.

[0032] The optical coupler 3 is a one-input, two-output optical coupler that branches the optical pulse branched by the optical coupler 1 into the waveguides WG3 and WG4 with the same intensity ratio, for example.

[0033] The inputs of the single-photon detectors PD1 to PD4 are connected to the optical waveguides WG1 to WG4, respectively. The single-photon detectors PD1 to PD4 detect photons incident through the optical waveguides WG1 to WG4, respectively. The single-photon detectors PD1 to PD4 then output detection signals D1 to D4 indicating the photon detection results to the signal processing unit 4.

[0034] The signal processing unit 4 performs predetermined signal processing on the detection results D1 to D4, and outputs a detection signal DET indicating the intensity of the light received by the single-photon detectors PD1 to PD4.

[0035] Next, the reception of a quantum signal by the receiving device 200 will be described. When a double optical pulse DLP in a state belonging to the Y basis is input to the receiving device 200, the relative phase of the double optical pulse is +π / 2 in the third state and −π / 2 in the fourth state. By designing the MZ interferometer 2 so that the phase difference between the phase of the light that has passed through arm A1 and the phase of the light that has passed through arm A2 is +π / 2, the relative phase of the double optical pulse is π (opposite phase) in the third state and 0 (in phase) in the fourth state. Therefore, the two states of the Y basis can be distinguished depending on whether the photon is detected by the single-photon detector PD1 or PD2.

[0036] When an optical pulse in a state belonging to the Z basis is incident on the receiving device 200, it can naturally be distinguished by the single-photon detectors PD3 and PD4. In the first state of the Z basis, only the pre-pulse PL1 is input to the single-photon detectors PD3 and PD4. In the second state, only the post-pulse PL2 is input to the single-photon detectors PD3 and PD4. Since it is known that the input timing of the post-pulse PL2 is delayed by Δt from the pre-pulse PL1, the two Z-basis states can be distinguished by detecting the pre-pulse PL1 at the appropriate timing with the single-photon detector PD3 and detecting the pre-pulse PL2 at the appropriate timing with the single-photon detector PD4.

[0037] In this configuration, as described above, the two states of the Y basis are identified by detecting the quantum signal output from the MZ interferometer 2. However, as described above, the visibility of the MZ interferometer 2 varies depending on the polarization state of the input light, which affects the detection accuracy of the quantum signal. Therefore, in this configuration, the processing device 10 calculates the polarization dependency of the visibility of the MZ interferometer, as will be described below.

[0038] The principle of calculating visibility in this embodiment will be described. Fig. 3 is a diagram showing the propagation of light in an MZ interferometer. The multiplexer / demultiplexer M1 branches the double optical pulse DLP into arms A1 and A2 at a 50:50 intensity ratio. Here, the multiplexer / demultiplexer M1 is configured as a two-input, two-output multiplexer / demultiplexer. The double optical pulse DLP is input to one input of the multiplexer / demultiplexer M1. No optical signal is input to the other input of the multiplexer / demultiplexer M1. The arm A1 is connected to the through output of the multiplexer / demultiplexer M1. The arm A2 is connected to the cross output of the multiplexer / demultiplexer M1.

[0039] The double optical pulse DLP propagating through the arm A1, which is the short path, is input to the through input IN1 of the multiplexer / demultiplexer M2. The double optical pulse DLP propagating through the arm A2, which is the long path, is input to the cross input IN2 of the multiplexer / demultiplexer M2. A central pulse is output from the through output OUT1 of the multiplexer / demultiplexer M2, resulting from interference in antiphase between the post pulse PL2 that has passed through the arm A1 and the pre pulse PL1 that has passed through the arm A2 and been given a delay Δt. Two adjacent pulses on either side of the central pulse are output randomly from the through output OUT1 or the cross output OUT2. A central pulse is output from the cross output OUT2 of the multiplexer / demultiplexer M2, resulting from interference in inphase between the post pulse PL2 that has passed through the arm A1 and the pre pulse PL1 that has passed through the arm A2 and been given a delay Δt. Two adjacent pulses on either side of the central pulse are output randomly from the through output OUT1 or the cross output OUT2.

[0040] The polarization state of the double optical pulse DLP at the input of the multiplexer / demultiplexer M1 is expressed by the following equation in Jones matrix notation.

[0041] The length of the arm A1, which is the short path, is set to L. The length of the arm A2, which is the long path, is set to L+ΔL. The frequency of the double light pulse TLP is set to f ０ Let n be the refractive index of the waveguide, and c be the speed of light in a vacuum. Then, the transfer matrix U of arm A2 is ｌｏｎｇ is expressed by the following formula: Transfer matrix U of arm A1 ｓｈｏｒｔ is expressed by the following formula:

[0042] Therefore, the optical intensity of the center pulse at the through output OUT1 of the multiplexer / demultiplexer M2 is expressed by the following equation. In addition, φ １ is expressed by the following formula: The optical intensity of the center pulse at the cross output OUT2 of the multiplexer / demultiplexer M2 is expressed by the following equation. In addition, φ ２ is expressed by the following formula:

[0043] Therefore, when the input doublet optical pulse DLP is in an arbitrary polarization state, the optical intensity of the central pulse at the through output OUT1 is expressed by the following equation using the Jones vector coefficient α indicating the polarization state. In the formula, the values ​​are defined as follows:

[0044] From the above, the visibility V of the MZ interferometer 2 is expressed by the following formula: Here, η is the amount of optical intensity mismatch, and is defined by the following equation: The amount of optical intensity mismatch η is an amount that indicates the optical intensity mismatch between two pulse beams when the pulse beams propagating through the two arms A1 and A2 of the Mach-Zehnder interferometer 2 interfere with each other in the multiplexer / demultiplexer M2. The light intensity of the double light pulse DLP is I ０ Then, the output light intensity ratio ΔI, which is the ratio of the light intensity at the through output OUT1 to the light intensity at the cross output OUT2, is expressed by the following equation. The numerator and denominator of the light intensity mismatch amount η are R １ R ２ Dividing by gives equation

[16] . Therefore, as can be seen from equation

[16] , it can be understood that the optical intensity mismatch amount η can be calculated using the output optical intensity ratio ΔI. Then, by applying the calculated optical intensity mismatch amount η to equation

[13] , it is possible to calculate the visibility V in any polarization state.

[0045] Next, a description will be given of the configuration and operation of the processing device 10. Fig. 4 is a block diagram showing a schematic configuration of a processing device according to an embodiment.

[0046] The processing device 10 includes an information reading unit 11, a polarization mode phase mismatch amount calculation unit 12, a light intensity mismatch amount calculation unit 13, and a visibility calculation unit 14.

[0047] The processing device 10 may have a means for reading information used to calculate the visibility V. FIG. 5 is a block diagram schematically showing the configuration of a processing device according to one embodiment. As shown in FIG. 5, the processing device 10 may have an information reading unit 11 that reads information used to calculate the visibility V. Below, an example will be described in which the processing device has the information reading unit 11. However, this does not mean that it is essential for the processing device to have the information reading unit 11.

[0048] The operation of the processing device will be described below: Fig. 6 is a flowchart showing the visibility calculation operation in the processing device according to one embodiment.

[0049] As shown in step S11 of FIG. 6, the information reading unit 11 reads the birefringence B of the waveguide, the optical path length difference ΔL, and the input optical frequency f ０ And the output light intensity ratio ΔI is read.

[0050] Birefringence B of the waveguide, optical path length difference ΔL, and input optical frequency f ０ The user of the processing device 10 may input these values ​​to the information reading unit 11 via an input means (not shown). ０ may be stored in advance in a storage means (not shown). In this case, the information reading unit 11 can read the birefringence B of the waveguide, the optical path length difference ΔL, and the input optical frequency f ０ may be read from the storage means.

[0051] The output light intensity ratio ΔI may be included in the detection signal DET output by the signal processing unit 4. Alternatively, the output light intensity ratio ΔI may be stored in advance in a storage means (not shown) based on the detection signal DET output by the signal processing unit 4. In this case, the information reading unit 11 may read the output light intensity ratio ΔI from the storage means at any timing.

[0052] 6, the polarization mode phase mismatch calculation unit 12 calculates the polarization mode phase mismatch Δφ based on the following equation: The polarization mode phase mismatch Δφ shown in equation

[11] is an amount that represents the difference in phase condition between two orthogonal polarization modes of light input to the Mach-Zehnder interferometer 2 when the light in each polarization mode propagates through two arms A1 and A2 of the Mach-Zehnder interferometer 2 having an optical path length difference and interferes in the multiplexer / demultiplexer M2. Here, c is the speed of light in a vacuum.

[0053] As shown in step S13 of FIG. 6, the light intensity mismatch calculation unit 13 calculates the light intensity mismatch η using equation

[16] .

[0054] 6, the visibility calculation unit 14 applies the calculated Δφ and η to equation

[13] to calculate the visibility V. This makes it possible to calculate the visibility V in which the fluctuation in the polarization state due to the birefringence of the waveguide is reflected by the Jones vector coefficient α.

[0055] As described above, according to this configuration, it is possible to estimate the polarization dependence of the visibility V of the MZ interferometer used to receive the quantum signal used in quantum key distribution.

[0056] In the first embodiment, the birefringence B of the waveguide, the optical path length difference ΔL, and the input optical frequency f ０ The visibility V was calculated using the polarization mode phase mismatch amount Δφ calculated based on the above equation. However, the method for calculating the visibility V is not limited to this. In this embodiment, a processing device will be described that calculates the visibility V using the polarization mode phase mismatch amount Δφ calculated by a method different from that of the first embodiment.

[0057] In the processing device according to the second embodiment, when calculating the polarization mode phase mismatch amount Δφ, the resonance frequency interval f ＦＳＲ and polarization dependent frequency shift Δf ＰＤ7 is a diagram showing the relationship between the resonant frequency interval and the polarization dependent frequency shift. When light propagates through a medium, due to the influence of the optical anisotropy of the medium, for example, birefringence occurring in an optical waveguide, the orthogonal vertically polarized waves L ＴＭ and horizontal polarization L ＴＥ There is a polarization dependent frequency shift Δf ＰＤ In addition, due to the influence of the light propagation path, the intensity of the output light varies periodically depending on the frequency of the light. The period of this frequency-dependent fluctuation in the intensity of the output light is the resonant frequency interval f ＦＳＲ is.

[0058] Resonant frequency interval f ＦＳＲ and polarization dependent frequency shift Δf ＰＤ may be obtained by measuring the target system in advance. ＦＳＲ and polarization dependent frequency shift Δf ＰＤ may be calculated by simulation or the like at the system design stage.

[0059] The configuration and operation of a processing device according to a second embodiment will be described. Fig. 8 is a block diagram schematically showing the configuration of a processing device according to an embodiment. Fig. 9 is a flowchart of a visibility calculation operation in a processing device according to an embodiment. A processing device 20 shown in Fig. 8 has a configuration in which the polarization mode phase mismatch amount calculation unit 12 of the processing device 10 is replaced with a polarization mode phase mismatch amount calculation unit 22. Other configurations of the processing device 20 are similar to those of the processing device 10, so duplicated explanations will be omitted.

[0060] As shown in step S21 of FIG. 9, the information reading unit 11 reads the resonant frequency interval (FSR: Free Spectral Range) f ＦＳＲ , polarization dependent frequency shift Δf ＰＤ , input optical frequency f ０ And the output light intensity ratio ΔI is read.

[0061] Resonant frequency interval f ＦＳＲ and polarization dependent frequency shift Δf ＰＤ The user of the processing device 20 may input the resonant frequency interval f to the information reading unit 11 via an input means (not shown).ＦＳＲ and polarization dependent frequency shift Δf ＰＤ may be stored in advance in a storage means (not shown). In this case, the information reading unit 11 can read the resonance frequency interval f ＦＳＲ and polarization dependent frequency shift Δf ＰＤ may be read from the storage means.

[0062] As shown in step S22 of FIG. 9, the polarization mode phase mismatch calculation unit 22 calculates the polarization mode phase mismatch Δφ based on the following equation.

[0063] Step S23 in FIG. 9 showing the operation of the light intensity mismatch amount calculation unit 13 is the same as step S13 in FIG. 6, so a duplicated description will be omitted.

[0064] Step S24 in FIG. 9 showing the operation of the visibility calculation unit 14 is the same as step S14 in FIG. 6, so a duplicated description will be omitted.

[0065] As described above, according to this configuration, similarly to the first embodiment, it is possible to estimate the visibility V of the MZ interferometer used to receive an optical signal used in quantum key distribution.

[0066] Third Embodiment In a general method, since it is not possible to estimate the visibility of a Mach-Zehnder interferometer, a method is used in which a specific visibility value is assigned as a known parameter to estimate the QBER. However, this method does not allow physical understanding of the influence of the polarization dependency of the MZ interferometer on the QBER. Therefore, there is a problem in that it is not possible to obtain sufficient information to obtain a physical perspective for improving the polarization dependency of the MZ interferometer and suppressing the QBER.

[0067] Furthermore, when determining the required device parameters based on the QKD system design, this method requires repeatedly measuring the QBER through experiments or numerical simulations while simulating all possible SOPs of the input light. This necessitates determining the required device parameters through trial and error, which requires a huge amount of time to design the system.

[0068] In contrast, with the processing device according to the above-described embodiment, the polarization dependency of the visibility V can be specifically obtained. Therefore, in this embodiment, a processing device will be described that further calculates the probability density functions of the visibility V and QBER based on the visibility V calculated in the above-described embodiment. With this configuration, the probability density functions of the visibility V and QBER are calculated based on the visibility V that reflects the polarization dependency, so the polarization dependency is also reflected in the probability density functions of the visibility V and QBER. This makes it possible to evaluate the variations in the visibility V and QBER due to the polarization state.

[0069] Fig. 10 is a block diagram schematically showing the configuration of a processing device according to an embodiment. Fig. 11 is a flowchart of the operation of the processing device according to an embodiment. The processing device 30 in Fig. 10 has a configuration in which a visibility probability density function calculation unit 15 and a QBER probability density function calculation unit 16 are further provided in the processing device 10. In Fig. 10, for simplicity of the drawing, the probability density function is abbreviated as PDF (Probability Density Function).

[0070] In this embodiment, as shown in step S31 of FIG. 11, the information reading unit 11 reads the birefringence B of the waveguide, the optical path length difference ΔL, and the input optical frequency f ０ In addition to the output light intensity ratio ΔI, the ratio γ of the photon detection rate to the dark count rate is also read. The photon detection rate at the receiver is P Ｓ , dark count rate P ｄ Then, the ratio γ of the photon detection rate to the dark count rate is expressed by the following equation:

[0071] The ratio γ of the photon detection rate to the dark count rate may be provided to the information reading unit 11 by a user of the processing device 30 via an input means (not shown). Alternatively, the ratio γ of the photon detection rate to the dark count rate may be stored in advance in a storage means (not shown). In this case, the information reading unit 11 may read the ratio γ of the photon detection rate to the dark count rate from the storage means at any timing.

[0072] The information reading unit 11 outputs the ratio γ of the read photon detection rate to the dark count rate to the QBER probability density function calculation unit 16 .

[0073] Steps S32 to S34 in Figure 11, which show the operations of the polarization mode phase mismatch calculation unit 12, the light intensity mismatch calculation unit 13, and the visibility calculation unit 14, are similar to steps S11 to S13 in Figure 6, respectively, and therefore redundant explanations will be omitted.

[0074] 11, the visibility probability density function calculation unit 15 calculates the probability density function of the visibility V using the polarization mode phase mismatch amount Δφ calculated by the polarization mode phase mismatch amount calculation unit 12 and the optical intensity mismatch amount η calculated by the optical intensity mismatch amount calculation unit 13. The calculation of the probability density function of the visibility V will be described below.

[0075] As described above, the distribution of the visibility V is defined by the following equation, with α as a variable. Here, α is a uniform distribution P in the range of 0 to 1, i.e., 0≦α≦1. α is a random variable that follows.

[0076] At this time, the probability density function P of the visibility V is Ｖ can be calculated as shown in the following formula: The range of values ​​that the visibility V can take is given by the following formula:

[0077] As shown in step S36 of FIG. 11, the QBER probability density function calculation unit 16 calculates the probability density function P Ｖ , the polarization mode phase mismatch amount Δφ, the optical intensity mismatch amount η, and the ratio γ of the photon detection rate to the dark count rate are used to calculate the probability density function P Ｅ Hereinafter, the calculation of the probability density function of QBER will be described.

[0078] The QBER value E is obtained by the following formula:

[0079] At this time, the probability density function P Ｅ is calculated using the following formula: At this time, the maximum value E of the range that the QBER value E can take is ｍａｘ and the minimum value E ｍａｘ is expressed by the following formula:

[0080] As described above, according to this configuration, it is possible to further obtain the probability density functions of the visibility V and the QBER.

[0081] 12 is a diagram showing a simulation of the probability density of QBER. In the QBER simulation, the dark count rate is assumed to be negligibly small, and the ratio γ of the photon detection rate to the dark count rate is set to 0. The light intensity mismatch amount η is set to 1. Under this condition, Δf included in the right side of equation

[19] ＰＤ / f ＦＳＲ The value of is changed in four stages, 0.5, 0.1, 0.15, and 0.2, and the probability density of QBER is calculated. Ｅ It can be seen that the probability density of QBER can be suitably estimated as shown in FIG.

[0082] Therefore, according to this configuration, by calculating the probability density functions of the visibility V and QBER, it is possible to evaluate the visibility V and QBER while taking into account the influence of the reception timing of the optical signal and the environment.

[0083] Other Embodiments The present disclosure has been described above with reference to the embodiments, but the present disclosure is not limited to the above-described embodiments. Various modifications that can be understood by those skilled in the art can be made to the configuration and details of the present disclosure within the scope of the present disclosure. Furthermore, each embodiment can be combined with other embodiments as appropriate.

[0084] In the above-described embodiment, the processing device is described as calculating the visibility, the visibility probability density function, and the QBER probability density function of an MZ interferometer used in a receiving device of a quantum key distribution system. However, the processing device according to the above-described embodiment may be used to calculate the interferometer visibility and the visibility probability density function of various devices such as a transmitting device used in a quantum key distribution system, or of any MZ interferometer used in a quantum key distribution system.

[0085] The processing device 30 according to the third embodiment has been described as the processing device 10 according to the first embodiment further provided with a visibility probability density function calculation unit 15 and a QBER probability density function calculation unit 16. However, by further providing the visibility probability density function calculation unit 15 and the QBER probability density function calculation unit 16 in the processing device 20 according to the second embodiment, a processing device that calculates the visibility probability density function and the QBER probability density function calculation unit may be configured.

[0086] In the above-described embodiments, the processing device according to the present disclosure has been described primarily as a hardware configuration, but this is not limited thereto. It is also possible to realize the processing device according to the present disclosure by having a computer execute a computer program to perform any process. These processes may be realized by having a computer including at least one processor (e.g., a microprocessor, a CPU, a GPU, an MPU, or a DSP (Digital Signal Processor)) execute the program. Specifically, one or more programs including instructions for causing a computer to perform these algorithms related to transmission signal processing or reception signal processing may be created, and the programs may be supplied to the computer.

[0087] A computer program can be stored and provided to a computer using various types of non-transitory computer-readable media. Non-transitory computer-readable media include various types of tangible storage media. Examples of non-transitory computer-readable media include magnetic recording media (e.g., flexible disks, magnetic tapes, hard disk drives), magneto-optical recording media (e.g., magneto-optical disks), CD-ROMs (Read Only Memory), CD-Rs, CD-R / Ws, and semiconductor memories (e.g., mask ROMs, PROMs (Programmable ROMs), EPROMs (Erasable PROMs), flash ROMs, and RAMs (Random Access Memory)). The program may be provided to the computer by various types of transient computer-readable media. Examples of transient computer-readable media include electrical signals, optical signals, and electromagnetic waves. The transient computer-readable media can provide the program to the computer via a wired communication path such as an electrical wire or optical fiber, or via a wireless communication path.

[0088] An example of the configuration of a computer for realizing the processing device is shown below. FIG. 13 is a diagram showing an example of the configuration of a computer for realizing the processing device. The processing device can be realized by a computer 9000 such as a dedicated computer or a personal computer (PC). However, the computer does not need to be physically single, and may be multiple computers when performing distributed processing. As shown in FIG. 13, the computer 9000 includes, for example, a processor 9001, a ROM (Read Only Memory) 9002, a RAM (Random Access Memory) 9003, a storage unit 9004, a communication interface 9005, and a user interface 9006.

[0089] The processor 9001, ROM 9002, RAM 9003, storage unit 9004, communication interface 9005, and user interface 9006 are connected to each other so as to be able to communicate with each other via a bus 9007. Note that although explanation of the OS software for operating the computer is omitted, it is also installed in the computer 9000 as appropriate.

[0090] The ROM 9002 is configured by, for example, a nonvolatile semiconductor memory device, etc. The ROM 9002 stores information such as various programs used by the computer 9000.

[0091] The storage unit 9004 is configured with various storage devices such as a hard disk, a solid state disk, etc. Furthermore, the storage unit 9004 is not limited to a storage device installed in the computer 9000, but may be a storage device external to the computer 9000. The external storage device may be a cloud storage device connected to the computer 9000 via various communication means, for example, a network. The storage unit 9004 stores information such as various programs and data used by the computer 9000.

[0092] The RAM 9003 is configured by a volatile semiconductor memory device, etc. Programs, data, and other information used by the processor 9001 are loaded into the RAM 9003 from one or both of the ROM 9002 and the storage unit 9004 as appropriate.

[0093] The processor 9001 may be configured with, for example, a CPU (Central Processing Unit). Furthermore, the processor 9001 may include not only a CPU but also a GPU (Graphics Processing Unit). A GPU is suitable for performing routine processing in parallel, and by applying it to neural network processing, for example, it is possible to improve processing speed compared to a CPU. The processor 9001 executes various processes based on various programs stored in the ROM 9002 or various programs and data held in the RAM 9003, as appropriate. Furthermore, the processor 9001 may store data generated by the processing in the RAM 9003 or the storage unit 9004, as appropriate.

[0094] The communication interface 9005 is an interface that connects the computer 9000 to a communication network such as the Internet or an intranet via various wired communication means or wireless communication means, etc. This allows the computer 9000 to communicate with other devices, systems, sensors, etc. that are connected to the communication network.

[0095] The user interface 9006 includes, for example, a display unit that provides information so that the user can recognize it using a display device or the like, and an audio output unit that outputs audio. The user interface 9006 also includes an input unit that allows the user to input information to the computer 9000 by operating it, such as a keyboard, a mouse, or a touch panel. The user interface 9006 may also include devices such as sensors that obtain information useful to the user.

[0096] Although the computer 9000 has been described as a single device here, this is merely an example. The computer 9000 may be composed of multiple physically separated devices. Some of the multiple devices may be portable devices, and the other devices may be stationary devices.

[0097] Each drawing is merely an example for describing one or more embodiments. Each drawing may not relate to only one particular embodiment, but may also relate to one or more other embodiments. As will be understood by those skilled in the art, various features or steps described with reference to any one drawing can be combined with features or steps shown in one or more other drawings to create, for example, an embodiment not explicitly shown or described. Not all features or steps shown in any one drawing are necessary to describe an exemplary embodiment, and some features or steps may be omitted. The order of steps described in any drawing may be changed as appropriate.

[0098] A part or all of the above-described embodiments can be described as, but not limited to, the following supplementary notes.

[0099] (Supplementary Note 1) A processing device comprising: a polarization mode phase mismatch amount calculation means for calculating a polarization mode phase mismatch amount representing a difference in phase condition between light of two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of a Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; an optical intensity mismatch amount calculation means for calculating an optical intensity mismatch amount between two input pulse lights when input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and a visibility calculation means for calculating a dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the input light based on the polarization mode phase mismatch amount and the optical intensity mismatch amount.

[0100] (Supplementary Note 2) The polarization mode phase mismatch amount is Δφ, the optical intensity mismatch amount is η, and a Jones vector coefficient indicating the polarization state of the input light is α, where α is a random variable that follows a uniform distribution in the range of 0 to 1, and the visibility calculation means calculates the visibility V by the following formula: 2. The processing device of claim 1.

[0101] (Note 3) Let B be the birefringence of the medium of the path through which the input light passes, ΔL be the optical path length difference between the two arms, and f be the frequency of the input light.０ , and the speed of light is c, the polarization mode phase mismatch amount calculation means calculates the polarization mode phase mismatch amount Δφ by the following formula: 3. The processing device of claim 2.

[0102] (Note 4) The resonant frequency interval when the input pulse light interferes in the multiplexer / demultiplexer is defined as f ＦＳＲ , the polarization dependent frequency shift between the two polarization modes is Δf ＰＤ and the polarization mode phase mismatch amount calculation means calculates the polarization mode phase mismatch amount Δφ by the following formula: 3. The processing device of claim 2.

[0103] (Supplementary Note 5) The light intensity mismatch amount calculation means calculates the light intensity mismatch amount ΔI by the following formula, where ΔI is the intensity difference between the two input pulsed lights: 5. The processing device of claim 3 or 4.

[0104] (Supplementary Note 6) The processing device according to Supplementary Note 5, wherein the Mach-Zehnder interferometer is provided in a receiving means for a quantum signal based on the BB84 protocol, and the quantum signal consisting of an optical pulse is input thereto.

[0105] (Supplementary Note 7) A visibility probability density function means for calculating a probability density function of the visibility based on the calculated visibility by the following formula: and quantum bit error rate probability density function means for calculating a quantum bit error rate probability density function by the following formula based on the calculated probability density function of the visibility, γ is the photon detection rate P when detecting the quantum signal. Ｓ and dark count rate P ｄ and is expressed by the following formula: 7. The processing device of claim 6.

[0106] (Supplementary Note 8) A method for detecting the dependence of the visibility of a quantum signal of two orthogonal polarization modes of input light on the polarization of the quantum signal when the light propagates through two arms of the Mach-Zehnder interferometer having an optical path length difference and interferes in a multiplexer / demultiplexer, comprising: a transmitting device for transmitting a quantum signal consisting of two successive optical pulses based on a BB84 protocol; a receiving device for outputting a detection signal obtained by decoding the quantum signal using a Mach-Zehnder interferometer; and a processing device for calculating the dependence of the visibility of the Mach-Zehnder interferometer on the polarization of the quantum signal based on the detection signal, a polarization mode phase mismatch amount calculation means for calculating a polarization mode phase mismatch amount that indicates a difference in phase condition between light beams; a light intensity mismatch amount calculation means for calculating a light intensity mismatch amount between two input pulse lights when the input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere with each other in the multiplexer / demultiplexer; and a visibility calculation means for calculating a dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the quantum signal based on the polarization mode phase mismatch amount and the light intensity mismatch amount.

[0107] (Supplementary Note 9) The polarization mode phase mismatch amount is Δφ, the optical intensity mismatch amount is η, and a Jones vector coefficient indicating the polarization state of the input light is α, where α is a random variable that follows a uniform distribution in the range of 0 to 1, and the visibility calculation means calculates the visibility V by the following formula: 9. The quantum communication system of claim 8.

[0108] (Supplementary Note 10) Let B be the birefringence of the medium of the path through which the input light passes, ΔL be the optical path length difference between the two arms, and f be the frequency of the input light. ０ , and the speed of light is c, the polarization mode phase mismatch amount calculation means calculates the polarization mode phase mismatch amount Δφ by the following formula: 10. The quantum communication system of claim 9.

[0109] (Note 11) The resonant frequency interval when the input pulse light interferes in the multiplexer / demultiplexer is defined as f ＦＳＲ , the polarization dependent frequency shift between the two polarization modes is Δf ＰＤand the polarization mode phase mismatch amount calculation means calculates the polarization mode phase mismatch amount Δφ by the following formula: 10. The quantum communication system of claim 9.

[0110] (Supplementary Note 12) The light intensity mismatch amount calculation means calculates the light intensity mismatch amount ΔI by the following formula, where ΔI is the intensity difference between the two input pulsed lights: 12. The quantum communication system according to claim 10 or 11.

[0111] (Supplementary Note 13) The quantum communication system according to Supplementary Note 12, wherein the Mach-Zehnder interferometer is provided in a receiving means for a quantum signal based on the BB84 protocol, and the quantum signal consisting of an optical pulse is input thereto.

[0112] (Supplementary Note 14) A visibility probability density function means for calculating a probability density function of the visibility based on the calculated visibility by the following formula: and quantum bit error rate probability density function means for calculating a quantum bit error rate probability density function by the following formula based on the calculated probability density function of the visibility, γ is the photon detection rate P when detecting the quantum signal. Ｓ and dark count rate P ｄ and is expressed by the following formula: 14. The quantum communication system of claim 13.

[0113] (Supplementary Note 15) A processing method comprising: calculating a polarization mode phase mismatch amount representing a difference in phase condition between light of two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of a Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; calculating an optical intensity mismatch amount between two input pulse lights when input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and calculating a dependency of visibility of the Mach-Zehnder interferometer on the polarization state of the input light based on the polarization mode phase mismatch amount and the optical intensity mismatch amount.

[0114] (Supplementary Note 16) The polarization mode phase mismatch amount is Δφ, the optical intensity mismatch amount is η, and a Jones vector coefficient indicating the polarization state of the input light is α, where α is a random variable that follows a uniform distribution in the range of 0 to 1, and the visibility V is calculated by the following formula: 16. The processing method of claim 15.

[0115] (Supplementary Note 17) Let B be the birefringence of the medium of the path through which the input light passes, ΔL be the optical path length difference between the two arms, and f be the frequency of the input light. ０ , the speed of light is c, and the polarization mode phase mismatch amount Δφ is calculated by the following formula: 17. The processing method of claim 16.

[0116] (Appendix 18) The resonance frequency interval when the input pulse light interferes in the multiplexer / demultiplexer is defined as f ＦＳＲ , the polarization dependent frequency shift between the two polarization modes is Δf ＰＤ The polarization mode phase mismatch amount Δφ is calculated by the following formula: 17. The processing method of claim 16.

[0117] (Supplementary Note 19) The intensity difference between the two input pulsed lights is ΔI, and the light intensity mismatch amount ΔI is calculated by the following formula: 19. The processing method according to claim 17 or 18.

[0118] (Supplementary Note 20) A program that causes a computer to execute the following processes: calculating a polarization mode phase mismatch amount that represents a difference in phase condition between light of two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of a Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; calculating an optical intensity mismatch amount between two input pulse lights when input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and calculating a dependency of visibility of the Mach-Zehnder interferometer on the polarization state of the input light based on the polarization mode phase mismatch amount and the optical intensity mismatch amount.

[0119] REFERENCE SIGNS LIST 1 Optical coupler 2 MZ interferometer 3 Optical coupler 4 Signal processing unit 10, 20, 30 Processing device 11 Information reading unit 12, 22 Polarization mode phase mismatch amount calculation unit 13 Light intensity mismatch amount calculation unit 14 Visibility calculation unit 15 Visibility probability density function calculation unit 16 QBER probability density function calculation unit 100 Transmitting device 200 Receiving device 300, 400 Transmission path 1000 Quantum key distribution system 9000 Computer 9001 Processor 9002 ROM 9003 RAM 9004 Storage unit 9005 Communication interface 9006 User interface 9007 Bus A1, A2 Arm DLP Double optical pulse IN1 Through input IN2 Cross input M1 Multiplexer / Demultiplexer M2 Multiplexer / Demultiplexer OUT1 Through output OUT2 Cross output PD1 to PD4 Single photon detector TLP Triple optical pulse V Visibility WG1 to WG6 Optical waveguide

Claims

1. A processing device comprising: a polarization mode phase mismatch amount calculation means for calculating a polarization mode phase mismatch amount representing a difference in phase condition between light of two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of a Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; an optical intensity mismatch amount calculation means for calculating an optical intensity mismatch amount between two input pulse lights when input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and a visibility calculation means for calculating the dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the input light based on the polarization mode phase mismatch amount and the optical intensity mismatch amount.

2. The polarization mode phase mismatch amount is Δφ, the optical intensity mismatch amount is η, and a Jones vector coefficient indicating the polarization state of the input light is α, where α is a random variable that follows a uniform distribution in the range of 0 to 1, and the visibility calculation means calculates the visibility V by the following formula: The processing device of claim 1 .

3. Let B be the birefringence of the medium through which the input light passes, ΔL be the optical path length difference between the two arms, and f be the frequency of the input light. ０ , where c is the speed of light, and the polarization mode phase mismatch calculation means calculates the polarization mode phase mismatch Δφ by the following formula: The processing device according to claim 2 .

4. The resonant frequency interval when the input pulse light interferes in the multiplexer / demultiplexer is defined as f ＦＳＲ , the polarization dependent frequency shift between the two polarization modes is Δf ＰＤ The polarization mode phase mismatch amount calculation means calculates the polarization mode phase mismatch amount Δφ by the following formula: The processing device according to claim 2 .

5. The intensity difference between the two input pulsed lights is defined as ΔI, and the light intensity mismatch amount calculation means calculates the light intensity mismatch amount ΔI by the following formula: The processing device according to claim 3 or 4.

6. The processing device according to claim 5, wherein the Mach-Zehnder interferometer is provided in a receiving means for a quantum signal based on the BB84 protocol, and the quantum signal consisting of an optical pulse is input thereto.

7. A visibility probability density function means for calculating a probability density function of the visibility based on the calculated visibility by the following formula: and quantum bit error rate probability density function means for calculating a quantum bit error rate probability density function by the following formula based on the calculated probability density function of the visibility, γ is the photon detection rate P when detecting the quantum signal. Ｓ and dark count rate P ｄ and is expressed by the following formula: The processing device of claim 6 .

8. A system comprising: a transmitting device that transmits a quantum signal consisting of a double optical pulse based on the BB84 protocol; a receiving device that outputs a detection signal obtained by decoding the quantum signal using a Mach-Zehnder interferometer; and a processing device that calculates the dependency of the visibility of the Mach-Zehnder interferometer on the polarization of the quantum signal based on the detection signal; a polarization mode phase mismatch amount calculating means that calculates a polarization mode phase mismatch amount that represents a difference in phase condition between light of two polarization modes in two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of the Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; an optical intensity mismatch amount calculating means that calculates an optical intensity mismatch amount between the two input pulse lights when input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and a visibility calculating means that calculates the dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the quantum signal based on the polarization mode phase mismatch amount and the optical intensity mismatch amount. Quantum communication systems.

9. The polarization mode phase mismatch amount is Δφ, the optical intensity mismatch amount is η, and a Jones vector coefficient indicating the polarization state of the input light is α, where α is a random variable that follows a uniform distribution in the range of 0 to 1, and the visibility calculation means calculates the visibility V by the following formula:

9. The quantum communication system of claim 8.

10. Let B be the birefringence of the medium through which the input light passes, ΔL be the optical path length difference between the two arms, and f be the frequency of the input light. ０ , where c is the speed of light, and the polarization mode phase mismatch calculation means calculates the polarization mode phase mismatch Δφ by the following formula:

10. The quantum communication system of claim 9.

11. The resonant frequency interval when the input pulse light interferes in the multiplexer / demultiplexer is defined as f ＦＳＲ , the polarization dependent frequency shift between the two polarization modes is Δf ＰＤ The polarization mode phase mismatch amount calculation means calculates the polarization mode phase mismatch amount Δφ by the following formula:

10. The quantum communication system of claim 9.

12. The intensity difference between the two input pulsed lights is defined as ΔI, and the light intensity mismatch amount calculation means calculates the light intensity mismatch amount ΔI by the following formula:

12. A quantum communication system according to claim 10 or 11.

13. The quantum communication system according to claim 12, wherein the Mach-Zehnder interferometer is provided in a receiving means for a quantum signal based on the BB84 protocol, and the quantum signal consisting of an optical pulse is input thereto.

14. A visibility probability density function means for calculating a probability density function of the visibility based on the calculated visibility by the following formula: and quantum bit error rate probability density function means for calculating a quantum bit error rate probability density function by the following formula based on the calculated probability density function of the visibility, γ is the photon detection rate P when detecting the quantum signal. Ｓ and dark count rate P ｄ and is expressed by the following formula:

14. The quantum communication system of claim 13.

15. A processing method comprising: calculating a polarization mode phase mismatch amount representing a difference in phase condition between light of two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of a Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; calculating an optical intensity mismatch amount between two input pulse lights when input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and calculating the dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the input light based on the polarization mode phase mismatch amount and the optical intensity mismatch amount.

16. The polarization mode phase mismatch amount is Δφ, the optical intensity mismatch amount is η, and the Jones vector coefficient indicating the polarization state of the input light is α, where α is a random variable that follows a uniform distribution in the range of 0 to 1, and the visibility V is calculated by the following formula:

16. The method of claim 15.

17. Let B be the birefringence of the medium through which the input light passes, ΔL be the optical path length difference between the two arms, and f be the frequency of the input light. ０ , the speed of light is c, and the polarization mode phase mismatch amount Δφ is calculated by the following formula:

17. The method of claim 16.

18. The resonant frequency interval when the input pulse light interferes in the multiplexer / demultiplexer is defined as f ＦＳＲ , the polarization dependent frequency shift between the two polarization modes is Δf ＰＤ The polarization mode phase mismatch amount Δφ is calculated by the following formula:

17. The method of claim 16.

19. The intensity difference between the two input pulse lights is ΔI, and the light intensity mismatch amount ΔI is calculated by the following formula:

19. The method of claim 17 or 18.

20. A program that causes a computer to execute the following processes: calculating a polarization mode phase mismatch amount that represents the difference in phase condition between light of two orthogonal polarization modes of input light when light of each polarization mode propagates through two arms of a Mach-Zehnder interferometer having an optical path length difference and interferes at a multiplexer / demultiplexer; calculating an optical intensity mismatch amount between two input pulse lights when the input pulse lights propagating through the two arms of the Mach-Zehnder interferometer interfere at the multiplexer / demultiplexer; and calculating the dependency of the visibility of the Mach-Zehnder interferometer on the polarization state of the input light based on the polarization mode phase mismatch amount and the optical intensity mismatch amount.

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