Method for improving the performance of a quantum key distribution system

Abstract

The present invention discloses a method for improving the performance of a quantum key distribution system. The method mainly includes: the sender prepares quantum states according to randomly selected optical intensity parameters, bit values, and bases, and transmits optical pulses to the receiver through a quantum channel; the receiver measures the received optical pulses according to randomly selected bases to generate original measurement data; after repeating several times, the bit data with consistent bases between the two parties is retained; parameter estimation is performed based on the screened bit data; the bit string is divided into bit blocks with the same length for advantage extraction, and relatively highly correlated key bit strings are extracted from weakly correlated bits, and error correction and privacy amplification operations are performed on the candidate keys to generate the final secure key. The present invention adopts an advantage extraction technique to improve the performance of a quantum key distribution system compatible with the post-pulse effect. The simulation results show that this method can significantly improve the performance of the quantum key distribution system in the case of being compatible with the post-pulse effect.

Description

Technical Field

[0001] The present invention relates to the field of quantum information technology, and in particular, to a method for improving the performance of a quantum key distribution system. Background Art

[0002] Based on the basic principles of quantum mechanics, quantum key distribution (QKD) provides an unconditionally secure key distribution method between two legitimate communication parties, Alice and Bob. The process of QKD can be divided into two stages: quantum signal transmission and post-processing. In the quantum signal transmission stage, Alice prepares a quantum state and transmits it to Bob, and Bob measures the received quantum state and generates a raw key. In the post-processing stage, Alice and Bob perform operations such as basis alignment, bit error rate estimation, key negotiation, error checking, and privacy amplification through a trusted authenticated classical channel to obtain a secure key. In recent years, QKD has made remarkable progress in theoretical research and technological development, gradually moving from the laboratory to practical application scenarios and becoming one of the key technologies in the fields of quantum information science and network security.

[0003] In 1984, Bennett and Brassard proposed the earliest QKD protocol, which was later called the BB84-QKD protocol. As the most representative and near-practical QKD protocol, the security of the BB84-QKD protocol under ideal conditions has been strictly proven. However, due to the existence of device defects, an actual QKD system cannot perfectly execute the theoretical protocol, which may introduce security vulnerabilities. For example, since it is difficult to prepare an ideal single-photon source, a weak coherent state light source is usually used instead. However, there are multi-photon events in the weak coherent state light source, which may cause eavesdroppers to use this event to implement a photon number splitting attack. An actual QKD system usually uses a single-photon avalanche diode as the detection device. However, as the operating frequency of the QKD system increases, the afterpulse effect of the single-photon avalanche diode becomes more obvious, resulting in an increasing deviation between the theoretical observable value and the true value of the actual system. Since the operating parameters of the QKD system are optimized through a theoretical model, the deviation of the model may have a greater impact on the system performance. To solve this problem, it has been verified that the afterpulse effect has historical memory, so a simulation model compatible with the afterpulse effect has been constructed in an actual QKD system. However, while improving the system security, this model also reduces the performance of the QKD system to a certain extent.

[0004] On the other hand, in the process of implementing the BB84-QKD system, the two communicating parties, Alice and Bob, need to calibrate their reference frames in real time, which increases the complexity of implementing the QKD system. Fortunately, by constructing a statistic independent of the reference frame deflection, researchers have proposed a reference-frame-independent quantum key distribution (RFI-QKD) protocol that can generate keys in the case of slow reference frame drift. In the RFI-QKD protocol, Alice and Bob randomly select X basis, Y basis, and Z basis to prepare and measure quantum states. In particular, recently, a research has proposed an RFI-QKD protocol based on estimating a statistic independent of the reference frame deflection from two joint events. This protocol is less sensitive to the statistical fluctuation effect in the actual system and has stronger robustness.

[0005] However, similar to the BB84-OKD system, the RFI-QKD system also has the afterpulse effect. Some scholars have proposed an RFI-QKD protocol compatible with the afterpulse effect to correct the deviation between the simulation model and the actual data, but this will also reduce the performance of the RFI-QKD system. Summary of the Invention

[0006] The present invention aims to solve at least one of the technical problems existing in the related art to some extent.

[0007] One object of the present invention is to provide a method for improving the performance of a quantum key distribution system, which increases the correlation of the screened keys through the advantage extraction technology, thereby reducing the negative impact of the afterpulse effect on the performance of the QKD system and improving the overall performance of the system.

[0008] Another object of the present invention is to provide the above method for improving the performance of a quantum key distribution system for application in actual BB84-QKD and RFI-QKD systems.

[0009] To achieve the above object, the present invention first provides a method for improving the performance of a quantum key distribution system, including the following steps:

[0010] S100. The sender Alice prepares a quantum state according to randomly selected light intensity parameters, bit values, and basis vectors, and transmits optical pulses to the receiver Bob through a quantum channel;

[0011] S200. Bob measures the received optical pulses according to randomly selected basis vectors to generate original measurement data;

[0012] S300. After Alice and Bob repeat steps S100-S200 several times, retain the bit data with the same basis vectors on both sides;

[0013] S400. Based on the filtered bit data, Alice and Bob calculate the counting rates and bit error rates of different light intensities under different basis vectors of the compatible pulse effect, and estimate the single-photon counting rate and single-photon bit error rate under different basis vectors of the compatible pulse effect;

[0014] S500. Alice and Bob respectively divide their bit strings into bit blocks of the same length, perform advantage extraction, and extract a key bit string with a relatively high degree of correlation from the weakly correlated bits;

[0015] S600. Perform error correction and privacy amplification operations on the candidate key to generate a final secure key.

[0016] A further preferred technical solution of the present invention is that the specific method of step S500 is:

[0017] S510. Alice and Bob divide their respective bit strings into bit blocks of length ; and ;

[0018] S520. Alice randomly selects a binary value , performs a bitwise exclusive OR of each bit in the bit block with , and sends the result to Bob through a classical channel;

[0019] S530. Bob performs a bitwise exclusive OR of the received result with his own bit block. If the result is all 1s or all 0s, he accepts the bit block and executes S540. Otherwise, he rejects the bit block and outputs a virtual symbol , ending this advantage extraction;

[0020] S540. Alice and Bob respectively retain the first bit block and of their respective initial bit strings as candidate keys.

[0021] Preferably, when this method is applied to a BB84-QKD system with a compatible pulse effect;

[0022] In step S100, Alice randomly selects a light intensity , a bit and a basis vector to prepare a quantum state and send it to Bob;

[0023] In step S200, Bob randomly selects a basis vector to measure the received optical pulse;

[0024] In step S400, Alice and Bob calculate different basis vectors of the compatible afterpulse effect at different light intensities of the counting rate and the bit error rate , and then, Alice and Bob respectively estimate the single-photon counting rate and the single-photon bit error rate under different basis vectors of the compatible afterpulse effect.

[0025] Preferably, the counting rate and the bit error rate at different light intensities under different basis vectors of the compatible afterpulse effect in step S400 are respectively:

[0026] ,

[0027] ,

[0028] where:

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] ,

[0034] ,

[0035] ,

[0036] ,

[0037] .

[0038] represents the response probability caused by optical pulses and dark counts, represents the response probability caused by afterpulses, is the background bit error rate, is the transmission efficiency between the sender Alice and the receiver Bob, is the dark count rate of the single-photon detector, is the probability of afterpulses occurring, is the total afterpulse rate, is the average response probability under different light intensities, is the probability of selecting a weak coherent state light source with a light intensity of is the probability of selecting a weak coherent state light source with a light intensity of is the probability that the sender Alice and the receiver Bob select a basis of

[0039] Preferably, the security key rate formula of the BB84-QKD system compatible with the post-pulse effect is expressed as:

[0040] ,

[0041] The constraint conditions are:

[0042] ,

[0043] ,

[0044] ,

[0045] ,

[0046] ,

[0047] ,

[0048] ,

[0049] ,

[0050] ,

[0051] ;

[0052] wherein, is the Shannon binary entropy function; is the error correction efficiency; is the probability that a single photon event is emitted by a signal state source with an intensity of represents the characteristics of the quantum channel controlled by Eve; and are the upper and lower bounds of and are the upper and lower bounds of is the length of the divided bit block; is the success probability of advantage extraction; Represents the characteristics of the quantum channel controlled by Eve after advantage extraction; It is the signal state bit error rate in the basis before the advantage extraction and compatible with the post-pulse effect; It is the signal state bit error rate in the basis after the advantage extraction and compatible with the post-pulse effect; Is the total signal state gain in the basis compatible with the post-pulse effect.

[0053] Preferably, when the above method is applied to an RFI-QKD system compatible with the post-pulse effect;

[0054] In step S100, Alice randomly selects the optical intensity , bit and basis to prepare the quantum state and send it to Bob;

[0055] In step S200, Bob randomly selects the basis to measure the received optical pulse; where the basis, basis, basis of Alice and Bob satisfy the conditions: , , , the subscripts A and B represent Alice and Bob respectively, represents the deflection angle of the reference frame;

[0056] After Alice and Bob repeat steps S100 - S200 several times in step S300, it is set that the bit data using the basis combinations , and by both parties is retained, while the bit data of other basis combinations is discarded; where represents the joint event that Alice prepares the quantum state with the basis while Bob measures the received quantum state with the basis and that Alice prepares the quantum state with the basis while Bob measures the received quantum state with the basis; represents the joint event that Alice prepares the quantum state with the basis while Bob measures the received quantum state with the basis and that Alice prepares the quantum state with the basis while Bob measures the received quantum state with the basis;

[0057] In step S400, Alice and Bob calculate the basis vector combinations of the compatible post-pulse effects , and under different light intensities of the counting rates , and , as well as the bit error rates , and ; Then, Alice and Bob respectively estimate the basis vector combinations of the compatible post-pulse effects , and under the single-photon counting rates , and , as well as the single-photon bit error rates , and .

[0058] Preferably, the basis vector combinations of the compatible post-pulse effects in step S400 , and under different light intensities of the counting rates , and , as well as the bit error rates , and are respectively:

[0059] ,

[0060] ,

[0061] ,

[0062] ,

[0063] ,

[0064] ,

[0065] where:

[0066] ,

[0067] ,

[0068] ,

[0069] ,

[0070] It refers to the probability when Alice prepares and sends a quantum state and Bob measures the quantum state at an optical intensity of ; is the background bit error rate; is the transmission efficiency between Alice and Bob; is the dark count rate of the single - photon detector; is the probability of after - pulse occurrence; is the total after - pulse rate; is the average response probability at different optical intensities; is the probability of selecting a weak coherent state light source with optical intensity, is the average response probability of all basis vector combinations when selecting a weak coherent state light source with optical intensity, and are the probabilities that Alice and Bob respectively select basis vectors and .

[0071] Preferably, the formula for the secure key rate of the RFI - QKD system compatible with the after - pulse effect is expressed as:

[0072] ,

[0073] The constraint conditions are:

[0074] ,

[0075] ,

[0076] ,

[0077] ,

[0078] ,

[0079] ,

[0080] ,

[0081] ,

[0082] ,

[0083] ,

[0084] Among them, is the Shannon binary entropy function; is the error correction efficiency; is the probability of a single - photon event emitted by a signal - state source with strength; represents the characteristics of the quantum channel controlled by Eve; and is the upper and lower bounds of, and are respectively the upper and lower bounds of the statistic ; is the length of the divided bit block; is the success probability of advantage extraction; represents the characteristics of the quantum channel controlled by Eve after advantage extraction; is the signal - state bit - error rate under the basis before compatible after - pulse effect and performing advantage extraction; is the signal - state bit - error rate under the basis after compatible after - pulse effect and performing advantage extraction; is the total gain of the signal state under the basis of compatible after - pulse effect.

[0085] On the other hand, the present invention provides an application of the above - mentioned method for improving the performance of a quantum key distribution system in a BB84 - QKD system. When this method is applied to a BB84 - QKD system compatible with after - pulse effect:

[0086] In step S100, Alice randomly selects the optical intensity , bit and basis to prepare a quantum state and send it to Bob;

[0087] In step S200, Bob randomly selects the basis to measure the received optical pulse;

[0088] In step S400, Alice and Bob calculate the count rates and bit - error rates of different optical intensities under different bases compatible with after - pulse effect. Then, Alice and Bob respectively estimate the single - photon count rates and single - photon bit - error rates under different bases compatible with after - pulse effect.

[0089] The count rates and bit - error rates of different optical intensities under different bases The models are respectively:

[0090] ,

[0091] ,

[0092] Among them:

[0093] ,

[0094] ,

[0095] ,

[0096] ,

[0097] ,

[0098] ,

[0099] ,

[0100] ,

[0101] .

[0102] represents the response probability caused by optical pulses and dark counts, represents the response probability caused by afterpulses, is the background bit error rate, is the transmission efficiency between the sender Alice and the receiver Bob, is the dark count rate of the single-photon detector, is the probability of afterpulse occurrence, is the total afterpulse rate, is the average response probability under different optical intensities, is the selection probability of the weak coherent state light source with the optical intensity, is the selection average response probability of all basis vectors when the weak coherent state light source with the optical intensity is selected, is the probability that the sender Alice and the receiver Bob select the basis vector .

[0103] Finally, the formula for the secure key rate of the BB84-QKD system compatible with the afterpulse effect is expressed as:

[0104] ,

[0105] The constraint condition is:

[0106] ,

[0107] ,

[0108] ,

[0109] ,

[0110] ,

[0111] ,

[0112] ,

[0113] ,

[0114] ,

[0115] ,

[0116] wherein, is the Shannon binary entropy function; is the error correction efficiency; is the probability of a single photon event emitted by a signal state source with intensity; represents the characteristics of the quantum channel controlled by Eve; and are the upper and lower bounds of, and are the upper and lower bounds of, is the length of the divided bit block; is the success probability of advantage extraction; represents the characteristics of the quantum channel controlled by Eve after advantage extraction; is the signal state bit error rate under the basis of is the signal state bit error rate under the basis of is the total signal state gain under the basis of

[0117] On the other hand, the present invention provides an application of the above method for improving the performance of a quantum key distribution system in an RFI-QKD system. When the above method is applied to an RFI-QKD system compatible with the post-pulse effect:

[0118] In step S100, Alice randomly selects the optical intensity , bit and basis to prepare a quantum state and send it to Bob;

[0119] In step S200, Bob randomly selects a basis to measure the received optical pulse; where the basis, basis, basis satisfy the conditions: , , , with subscripts A and B representing Alice and Bob respectively, representing the deflection angle of the reference frame;

[0120] After Alice and Bob repeat steps S100 - S200 several times in step S300, it is set that the bit data of the basis combinations , and will be retained, while the bit data of other basis combinations will be discarded; where represents the joint event that Alice prepares a quantum state with the basis while Bob measures the received quantum state with the basis and that Alice prepares a quantum state with the basis while Bob measures the received quantum state with the basis; represents the joint event that Alice prepares a quantum state with the basis while Bob measures the received quantum state with the basis and that Alice prepares a quantum state with the basis while Bob measures the received quantum state with the basis;

[0121] In step S400, Alice and Bob calculate the counting rates , and of different optical intensities under the basis combinations , and , as well as the bit error rates , and ; then, Alice and Bob respectively estimate the single - photon counting rates , and under the basis combinations , and , and the single - photon bit - error rate , and .

[0122] Among them, , and , and the bit - error rate , and The models of are respectively:

[0123] ,

[0124] ,

[0125] ,

[0126] ,

[0127] ,

[0128] ,

[0129] Among them:

[0130] ,

[0131] ,

[0132] ,

[0133] .

[0134] refers to the probability when the light intensity is , Alice prepares and sends the quantum state and Bob measures the quantum state ; is the background bit - error rate; is the transmission efficiency between Alice and Bob; is the dark - count rate of the single - photon detector; is the probability of after - pulse occurrence; is the total after - pulse rate; is the average response probability under different light intensities; is the probability of selecting the weak coherent state light source with the light intensity of , is the average response probability of all basis - vector combinations when selecting the weak coherent state light source with the light intensity of , and The probabilities that Alice and Bob respectively select the basis vectors and .

[0135] Finally, the formula for the secure key rate of the RFI-QKD system compatible with the post-pulse effect is expressed as:

[0136] ,

[0137] The constraint conditions are:

[0138] ,

[0139] ,

[0140] ,

[0141] ,

[0142] ,

[0143] ,

[0144] ,

[0145] ,

[0146] ,

[0147] .

[0148] Among them, is the Shannon binary entropy function; is the error correction efficiency; is the probability of a single-photon event emitted by the signal state source with intensity represents the characteristics of the quantum channel controlled by Eve; and are the upper and lower bounds of and are respectively the upper and lower bounds of the statistic ; is the length of the divided bit block; is the success probability of advantage extraction; represents the characteristics of the quantum channel controlled by Eve after advantage extraction; is the signal state bit error rate under the basis of compatible with the post-pulse effect and before performing advantage extraction; It is after being compatible with the post-pulse effect and performing advantage extraction The bit error rate of the signal state under the basis; It is for being compatible with the post-pulse effect The total gain of the signal state under the basis.

[0149] Beneficial effects: In order to reduce the negative impact of the post-pulse effect on the performance of the QKD system, the present invention applies an advantage extraction technique before the post-processing step to increase the correlation of the screened keys, thereby improving the overall performance of the QKD system. Through simulation verification, it is proved that the method of the present invention can significantly improve the performance of the actual QKD system compatible with the post-pulse effect. Description of the drawings

[0150] Figure 1 It is a flowchart of the advantage extraction method in the present invention.

[0151] Figure 2 In Embodiment 2 of the present invention, at the low bit error rate , the post-pulse rates are respectively and The performance simulation diagram of the BB84-QKD system;

[0152] Figure 2 In (a), it is a curve graph of the relationship between the key rate and the transmission distance between Alice and Bob; Figure 2 In (b), it is the optimal Value and the curve graph of the relationship with the transmission distance.

[0153] Figure 3 In Embodiment 2 of the present invention, at the low bit error rate , the post-pulse rates are respectively and The performance simulation diagram of the BB84-QKD system;

[0154] Figure 3 In (a), it is a curve graph of the relationship between the key rate and the transmission distance between Alice and Bob; Figure 3 In (b), it is the optimal Value and the curve graph of the relationship with the transmission distance.

[0155] Figure 4 In Embodiment 3 of the present invention, at the low bit error rate , the post-pulse rates are respectively and The performance simulation diagram of the RFI-QKD system;

[0156] Figure 4 In (a), it is a curve graph of the relationship between the key rate and the transmission distance between Alice and Bob; Figure 4 In (b), it is the optimal Relationship curve diagram of value and transmission distance.

[0157] Figure 5 In Embodiment 3 of the present invention, at a low bit error rate , the post-pulse rates are respectively and Performance simulation schematic diagram of the RFI-QKD system;

[0158] Figure 5 In (a), it is the relationship curve diagram of the key rate between Alice and Bob and the transmission distance; Figure 5 In (b), it is the relationship curve diagram of the optimal value and the transmission distance. Detailed implementation manners

[0159] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention, and they should not be construed as limiting the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for the purpose of description and cannot be construed as indicating or implying relative importance.

[0160] The following will describe Figures 1 - 5 a method for improving the performance of a quantum key distribution system provided by the present invention and its applications.

[0161] Embodiment 1: This embodiment provides a method for improving the performance of a quantum key distribution system.

[0162] The specific steps of this method are as follows:

[0163] State preparation: The sender Alice prepares a quantum state according to randomly selected light intensity parameters, bit values and bases, and transmits optical pulses to the receiver Bob through a quantum channel;

[0164] State measurement: Bob measures the received optical pulses according to randomly selected bases to generate original measurement data;

[0165] Basis alignment: After Alice and Bob repeat the above two steps a sufficient number of times, the bit data with consistent bases of both parties is retained;

[0166] Parameter estimation: Based on the filtered bit data, Alice and Bob calculate the counting rates and bit error rates of different light intensities under different bases that are compatible with the post-pulse effect, and estimate the single-photon counting rate and single-photon bit error rate under different bases that are compatible with the post-pulse effect;

[0167] Advantage extraction: Alice and Bob respectively divide their bit strings into bit blocks of the same length, perform advantage extraction, and extract a key bit string with a relatively high degree of correlation from the weakly correlated bits;

[0168] Error correction and privacy amplification: Perform error correction and privacy amplification operations on the candidate key to generate a final secure key.

[0169] In this embodiment, the Cascade protocol is used for error correction, and the hash function for realizing privacy amplification is the Toeplitz matrix.

[0170] In this embodiment, the overall process of the advantage extraction step is as Figure 1 shown, including:

[0171] (1), Alice and Bob divide their respective bit strings into bit blocks of length and ; ;

[0172] (2), Alice randomly selects a binary value , performs a bitwise exclusive OR of each bit in the bit block with , and sends the result to Bob through the classical channel;

[0173] (3), Bob performs a bitwise exclusive OR of the received result with his own bit block. If the result is all 1s or all 0s, accept the bit block and execute S540, otherwise reject the bit block and output the virtual symbol , and end this advantage extraction;

[0174] (4), Alice and Bob respectively retain the first bit blocks and of their respective initial bit strings as candidate keys.

[0175] Embodiment 2: An application of the above method in a BB84-QKD system.

[0176] When applying the method for improving the performance of the quantum key distribution system in Embodiment 1 to a BB84-QKD system compatible with the after-pulse effect:

[0177] During the state preparation process, Alice randomly selects the optical intensity , bit and basis to prepare a quantum state and send it to Bob;

[0178] During the state measurement process, Bob randomly selects the basis to measure the received optical pulse;

[0179] During the parameter estimation process, Alice and Bob calculate different basis vectors of the compatible afterpulse effect at different light intensities of the counting rate and the bit error rate , then, Alice and Bob respectively use the decoy state method to estimate the single photon counting rate at different basis vectors of the compatible afterpulse effect and the single photon bit error rate .

[0180] The different basis vectors of the compatible afterpulse effect at different light intensities of the counting rate and the bit error rate models are respectively:

[0181] ,

[0182] ,

[0183] where:

[0184] ,

[0185] ,

[0186] ,

[0187] ,

[0188] ,

[0189] ,

[0190] ,

[0191] ,

[0192] .

[0193] represents the response probability caused by optical pulses and dark counts, represents the response probability caused by afterpulses, is the background bit error rate, is the transmission efficiency between the sender Alice and the receiver Bob, is the dark count rate of the single photon detector, is the probability of generating afterpulses, is the total afterpulse rate, is the average response probability under different light intensities, is the probability of selecting a weak coherent state light source with a light intensity, is the probability of selecting a weak coherent state light source with a light intensity for the average response probability of all basis vectors, is the probability that the sender Alice and the receiver Bob select the basis vector .

[0194] Finally, the security key rate formula of the BB84-QKD system compatible with the post-pulse effect is expressed as:

[0195] ,

[0196] The constraint conditions are:

[0197] ,

[0198] ,

[0199] ,

[0200] ,

[0201] ,

[0202] ,

[0203] ,

[0204] ,

[0205] ,

[0206] .

[0207] Among them, is the Shannon binary entropy function; is the error correction efficiency; is the probability that a single photon event is emitted by a signal state source with an intensity; represents the characteristics of the quantum channel controlled by Eve; and are the upper and lower bounds of, and are the upper and lower bounds of, is the length of the divided bit block; is the success probability of advantage extraction; Represents the characteristics of the quantum channel controlled by Eve after advantage extraction; Is the bit error rate of the signal state under the basis that is compatible with the post-pulse effect and before performing advantage extraction ; Is the bit error rate of the signal state under the basis that is compatible with the post-pulse effect and after performing advantage extraction ; Is the total signal state gain under the basis that is compatible with the post-pulse effect ;

[0208] Based on Example 2, a simulation experiment was carried out, and the simulation parameters are as follows:

[0209] The detection efficiency of the single-photon detector ; The dark count rate of the single-photon detector ; The error correction efficiency ; The loss coefficient of the standard communication optical fiber link is ; The safety factor in the finite-length analysis is ; The total number of pulses sent by Alice is . Based on these parameters, a practical BB84-QKD system that is compatible with the post-pulse effect based on the advantage extraction technology was simulated, and the results are as shown in Figure 2 and Figure 3 ;

[0210] Figure 2 Is the bit error rate When, the simulation schematic diagram of the system performance of the BB84-QKD system when the post-pulse rates are respectively and ; Figure 2 In (a), it is the relationship curve diagram of the key rate between Alice and Bob and the transmission distance, where the total number of pulses is set to ; The solid line BB84-AD represents the secure key rate of the BB84-QKD system using the advantage extraction technology, and the dashed line BB84 represents the secure key rate of the BB84-QKD system without using the advantage extraction technology Figure 2 In (b), it is the relationship curve diagram of the optimal Value and the transmission distance

[0211] Figure 3 Is the bit error rate When, the simulation schematic diagram of the system performance of the BB84-QKD system when the post-pulse rates are respectively and ; Figure 3 In (a), it is the relationship curve diagram of the key rate between Alice and Bob and the transmission distance, where the total number of pulses is set to , the solid line BB84-AD represents the secure key rate of the BB84-QKD system using the advantage extraction technology, and the dashed line BB84 represents the secure key rate of the BB84-QKD system without using the advantage extraction technology. Figure 3 In (b) is the optimal Value versus transmission distance curve graph.

[0212] Through simulation verification, it is proved that by adopting the advantage extraction technology, the performance of the BB84-QKD system compatible with post-pulse can be significantly improved.

[0213] Example 3: An application of the above method in an RFI-QKD system.

[0214] When applying the method for improving the performance of the quantum key distribution system in Example 1 to an RFI-QKD system compatible with post-pulse effects:

[0215] During the state preparation process, Alice randomly selects the optical intensity , bit and basis to prepare the quantum state and send it to Bob;

[0216] During the state measurement process, Bob randomly selects the basis to measure the received optical pulse; where the basis, basis, basis satisfy the conditions: , , , the subscripts A and B represent Alice and Bob respectively, represents the deflection angle of the reference frame;

[0217] During the basis alignment process, it is set to retain the bit data of the basis vector combinations , and while discarding the bit data of other basis vector combinations; where represents the joint event that Alice prepares the quantum state with the basis while Bob measures the received quantum state with the basis and that Alice prepares the quantum state with the basis while Bob measures the received quantum state with the basis; represents the joint event that Alice prepares the quantum state with the basis while Bob measures the received quantum state with the basis and that Alice prepares the quantum state with the basis while Bob measures the received quantum state with the to measure the joint events of the received quantum states;

[0218] During the parameter estimation process, Alice and Bob calculate the basis combinations of the compatible post-pulse effects , and under different light intensities of the counting rates , and , as well as the bit error rates , and ; Then, Alice and Bob respectively use the decoy state method to estimate the single-photon counting rates , and under , and , as well as the single-photon bit error rates , and .

[0219] Among them, , and , as well as the bit error rates , and 's models are respectively:

[0220] ,

[0221] ,

[0222] ,

[0223] ,

[0224] ,

[0225] ,

[0226] Among them:

[0227] ,

[0228] ,

[0229] ,

[0230] .

[0231] It refers to the probability when the light intensity is and Alice prepares and sends the quantum state while Bob measures the quantum state ; is the background bit error rate; is the transmission efficiency between Alice and Bob; is the dark count rate of the single-photon detector; is the probability of afterpulse occurrence; is the total afterpulse rate; is the average response probability at different light intensities; is the probability of selecting the weak coherent state light source with light intensity, is the average response probability of all basis vector combinations when selecting the weak coherent state light source with light intensity, and are the probabilities that Alice and Bob respectively select the basis vectors and .

[0232] Finally, the formula for the secure key rate of the RFI-QKD system compatible with the afterpulse effect is expressed as:

[0233] ,

[0234] The constraint conditions are:

[0235] ,

[0236] ,

[0237] ,

[0238] ,

[0239] ,

[0240] ,

[0241] ,

[0242] ,

[0243] ,

[0244] .

[0245] Among them, is the Shannon binary entropy function; is the error correction efficiency; is The probability of a single - photon event emitted by a signal - state source with intensity; Represents the characteristics of the quantum channel controlled by Eve; and is The upper and lower bounds of, and are respectively the upper and lower bounds of the statistic ; Is the length of the divided bit block; Is the success probability of advantage extraction; Represents the characteristics of the quantum channel controlled by Eve after advantage extraction; Is the signal - state bit - error rate under the basis of compatible with the after - pulse effect and before performing advantage extraction; Is the signal - state bit - error rate under the basis of compatible with the after - pulse effect and after performing advantage extraction; Is the total signal - state gain under the basis of compatible with the after - pulse effect.

[0246] Based on Example 3, a simulation experiment was carried out, and the simulation parameters are as follows:

[0247] The detection efficiency of the single - photon detector ; The dark - count rate of the single - photon detector ; The error - correction efficiency ; The loss coefficient of the standard communication fiber link is ; The safety factor in the finite - length analysis is ; ; The total number of pulses sent by Aice is . Based on these parameters, the actual RFI - QKD system compatible with the after - pulse effect based on the advantage - extraction technology was simulated, and the results are as shown in Figure 4 and Figure 5 .

[0248] Figure 4 Is the base bit - error rate When the RFI - QKD system has after - pulse rates of and respectively, the schematic diagram of the system performance simulation. Figure 4 In (a), it is the curve graph of the relationship between the key rate and the transmission distance between Alice and Bob, where the total number of pulses is set to ; The solid line RFI - AD represents the secure key rate of the RFI - QKD system using the advantage - extraction technology, and the dashed line RFI represents the secure key rate of the RFI - QKD system without using the advantage - extraction technology. Figure 4 In (b), it is the curve graph of the relationship between the optimal value and the transmission distance.

[0249] Figure 5 For the base bit error rate When the RFI-QKD system has post-pulse rates of and respectively, the schematic diagram of the system performance simulation. Figure 5 In (a), it is the curve graph of the relationship between the key rate and the transmission distance between Alice and Bob, where the total number of pulses is set to ; the solid line RFI-AD represents the secure key rate of the RFI-QKD system using the advantage extraction technology, and the dashed line RFI represents the secure key rate of the RFI-QKD system without using the advantage extraction technology. Figure 5 In (b), it is the curve graph of the relationship between the optimal value and the transmission distance.

[0250] Through simulation verification, it is proved that by adopting the advantage extraction technology, the performance of the RFI-QKD system compatible with post-pulses can be significantly improved.

[0251] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for improving the performance of a quantum key distribution system, characterized in that: The following steps are involved: S100, the sender Alice prepares a quantum state according to the randomly selected light intensity parameters, bit values ​​and basis vectors, and transmits a light pulse to the receiver Bob through a quantum channel; S200, the receiver Bob measures the received optical pulse according to the randomly selected basis vector to generate original measurement data; S300: After the sender Alice and the receiver Bob repeat steps S100-S200 several times, the bit data with consistent basis vectors of both parties are retained; S400, based on the filtered bit data, the sender Alice and the receiver Bob calculate the count rate and bit error rate of different light intensities under different basis vectors of the compatible pulse effect, and estimate the single photon count rate and single photon bit error rate under different basis vectors of the compatible pulse effect; S500, the sender Alice and the receiver Bob respectively divide their bit strings into bit blocks of the same length, perform advantage extraction, and extract key bit strings with higher correlation from the weakly correlated bits; S600, performing error correction and privacy amplification operations on the candidate key to generate a final security key; This method is applied to the BB84-QKD system compatible with the after-pulse effect; In step S100, the sender Alice randomly selects light intensity l∈{u,v,w}, bit s∈{0,1} and basis vector ζ∈{Z,X} to prepare the quantum state and sends it to the receiver Bob; In step S200, the receiver Bob randomly selects a basis vector ζ∈{Z,X} to measure the received optical pulse; In step S400, the sender Alice and the receiver Bob calculate the count rates of different light intensities l under different basis vectors ζ of the compatible post-pulse effect. and bit error rate Then, the sender Alice and the receiver Bob respectively estimate the single photon counting rate under different basis vectors ζ of the compatible post-pulse effect and single photon bit error rate Count rate of different light intensities l under different basis vectors ζ compatible with post-pulse effect and bit error rate The models are: in: represents the response probability caused by light pulses and dark counts, represents the probability of response caused by the afterpulse, e d is the background bit error rate, η is the transmission efficiency between the sender Alice and the receiver Bob, Y ％ is the dark count rate of the single photon detector, P ap is the probability of a post-pulse, P a is the total afterpulse rate, is the average response probability under different light intensities, P l is the probability of selecting a weak coherent state light source with light intensity l, is the average response probability of all basis vectors when a weak coherent state light source with light intensity l is selected, P ζ is the probability that sender Alice and receiver Bob choose the basis vector ζ; This method is applied in RFI-QKD systems that are compatible with the after-pulse effect; In step S100, the sender Alice randomly selects the light intensity l∈{u,v,w}, the bit s∈{0,1} and the basis vector ζ ； = {Z ； ,X ； ,Y ； } to prepare the quantum state and send it to the receiver Bob; In step S200, the receiver Bob randomly selects a basis vector ζ < = {Z < ,X < ,Y < } to measure the received optical pulses; where the Z basis, X basis, and Y basis of the sender Alice and the receiver Bob satisfy the conditions: Z ； =Z < , X < =cosβX ； +sinβY ； , Y < =cosβY ； -sinβX ； , subscripts A and B represent the sender Alice and the receiver Bob respectively, and β represents the deflection angle of the reference system; In step S300, after the sender Alice and the receiver Bob repeat steps S100-S200 several times, they set the basis vector combination Z used by both parties. ； Z < , X ； X < Y ； Y < and X ； Y < Y ； X < The bit data of X is retained, while the bit data of other basis vector combinations are discarded; ； X < Y ； Y < represents the joint event of Alice preparing a quantum state using the X basis and Bob measuring the received quantum state using the X basis, and Alice preparing a quantum state using the Y basis and Bob measuring the received quantum state using the Y basis; X ； Y < Y ； X < represents the joint event of Alice preparing a quantum state using the X basis while Bob measures the received quantum state using the Y basis and Alice preparing a quantum state using the Y basis while Bob measures the received quantum state using the X basis; In step S400, the sender Alice and the receiver Bob calculate the basis vector combination X of the compatible post-pulse effect ； X < , X ； X < Y ； Y < and X ； Y < Y ； X < Count rate at different light intensities l and And bit error rate and Then, Alice and Bob estimate the basis vector combination Z that is compatible with the post-pulse effect. ； Z < , X ； X < Y ； Y < and X ； Y < Y ； X < Single photon counting rate under and and single photon bit error rate and 2. The method for improving the performance of a quantum key distribution system according to claim 1, characterized in that: The specific method of step S500 is: S510, the sender Alice and the receiver Bob divide their respective bit strings into bit blocks of length b (x1,…,x b ) and (y1,…,y b ); S520: The sender Alice randomly selects a binary value r, performs bitwise XOR on each bit in the bit block and r, and Sent to the receiver Bob via a classic channel; S530, the receiver Bob performs bitwise XOR on the received result and its own bit block. If the result is all 1 or all 0, the bit block is accepted and S540 is executed. Otherwise, the bit block is rejected and a virtual symbol is output. End the advantage extraction; S540, the sender Alice and the receiver Bob respectively retain the first bit blocks x1 and y1 of their respective initial bit strings as candidate keys.

3. The method for improving the performance of a quantum key distribution system according to claim 1, characterized in that: When this method is applied to a BB84-QKD system compatible with the after-pulse effect, the security key rate formula of the BB84-QKD system compatible with the after-pulse effect is expressed as: The constraints are: Where H(x) = -xlog " x-(1-x)log " (1-x) is the Shannon binary entropy function; f is the error correction efficiency; is the probability of a single photon emission event from a signal state source of intensity u; ％ ,λ1,λ " ,λ a represents the quantum channel characteristics controlled by Eve; and for The upper and lower bounds of and for The upper and lower bounds of , b is the length of the divided bit block; qsucc is the success probability of advantage extraction; represents the quantum channel characteristics controlled by Eve after advantage extraction; is the signal state bit error rate in the Z basis compatible with the post-pulse effect and before performing advantage extraction; is the signal state bit error rate in the Z basis after being compatible with the post-pulse effect and performing advantage extraction; is the total signal state gain in the Z basis compatible with the after-pulse effect.

4. The method for improving the performance of a quantum key distribution system according to claim 1, characterized in that: This method is applied to the RFI-QKD system compatible with the after-pulse effect: The basis vector combination Z compatible with the post-pulse effect in step S400 ； Z < , X ； X < Y ； Y < and X ； Y < Y ； X < Count rate at different light intensities l and And bit error rate and The models are: in: It means that when the light intensity is l, Alice prepares and sends the quantum state And Bob measures the quantum state The probability of e d is the background bit error rate; η is the transmission efficiency between Alice and Bob; Y ％ is the dark count rate of the single-photon detector; P ap is the probability of a post-pulse; P a is the total afterpulse rate; is the average response probability under different light intensities; P l is the probability of selecting a weak coherent state light source with light intensity l, is the average response probability of all basis vector combinations when a weak coherent state light source with light intensity l is selected, and Alice and Bob choose the basis vector ζ ； and < probability.

5. The method for improving the performance of a quantum key distribution system according to claim 4, characterized in that: When this method is applied to an RFI-QKD system compatible with the after-pulse effect, the security key rate formula of the RFI-QKD system compatible with the after-pulse effect is expressed as: The constraints are: Where H(x) = -xlog " x-(1-x)log " (1-x) is the Shannon binary entropy function; f is the error correction efficiency; is the probability of a single photon emission event from a signal state source of intensity u; ％ ,λ1,λ " ,λ a represents the quantum channel characteristics controlled by Eve; and for The upper and lower bounds of R f and R d are the upper and lower bounds of the statistic R respectively; b is the length of the divided bit block; q succ is the success probability of advantage extraction; represents the quantum channel characteristics controlled by Eve after advantage extraction; is the signal state bit error rate in the Z basis compatible with the post-pulse effect and before performing advantage extraction; is the signal state bit error rate in the Z basis after being compatible with the post-pulse effect and performing advantage extraction; is the total signal state gain in the Z basis compatible with the after-pulse effect.

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