Performance improvement method for double-independent quantum key distribution of actual reference system measurement equipment

Abstract

The invention discloses a method for improving the performance of double-independent quantum key distribution of actual reference system measurement equipment, belongs to the technical field of quantum key distribution (QKD), and aims to improve the performance of the double-independent quantum key distribution when non-ideal factors such as a post-pulse effect of a detector and finite sample statistical fluctuation are considered. The invention relates to a method and a system for improving the performance of a reference system measurement device by introducing an advantage extraction technology into a double independent quantum key distribution (RFI-MDI-QKD) protocol of the reference system measurement device. Simulation results show that when the post-pulse effect and the statistical fluctuation effect are considered, the advantage extraction method can effectively improve the security key rate and the security transmission distance of the RFI-MDI-QKD protocol on the premise of not changing optical hardware. According to the invention, a valuable reference technology can be provided for practical research of the RFI-MDI-QKD system.

Description

Technical Field

[0001] This invention relates to the fields of quantum communication and quantum cryptography, specifically to a method for improving the performance of dual-independent quantum key distribution in a practical reference frame measurement device. Background Technology

[0002] Based on the fundamental principles of quantum mechanics, quantum key distribution (QKD) provides information-theoretically secure keys between Alice and Bob. In recent years, QKD technology has made significant progress and has been gradually deployed in practical communication networks. However, the non-ideals of devices in real-world systems, such as reference frame drift, measurement device vulnerabilities, and finite impulses, pose various security threats and performance limitations to QKD systems.

[0003] To address the reference frame drift problem, the Reference-Frame Independent Quantum Key Distribution (RFI-QKD) protocol was proposed. To close security vulnerabilities in measurement devices, the Measurement-Device Independent Quantum Key Distribution (MDI-QKD) protocol was proposed. Building upon RFI-QKD and MDI-QKD, researchers combined RFI-QKD with MDI-QKD to propose the Reference-Frame Measurement-Device Dual Independent Quantum Key Distribution (RFI-MDI-QKD) protocol. This protocol not only possesses robustness against reference frame drift but also immunity to all measurement device vulnerabilities, thus exhibiting stronger overall security and practicality in complex real-world environments. Furthermore, a novel RFI-MDI-QKD protocol based on statistics that rely on fewer observables and are independent of reference frame drift was proposed. This protocol not only inherits all the advantages of the original RFI-MDI-QKD protocol but also exhibits better performance when considering finite code length effects.

[0004] Practical RFI-MDI-QKD systems typically employ single-photon avalanche detectors (SPADs) as their detection elements. However, the afterpulse effect of SPADs cannot be ignored. Furthermore, the statistical fluctuation effects caused by the finite pulses emitted in practical RFI-MDI-QKD systems also need to be carefully considered. Summary of the Invention

[0005] The present invention aims to at least partially solve one of the technical problems existing in the related art.

[0006] One objective of this invention is to provide a method for improving the performance of a reference frame measurement device dual independent quantum key distribution (RFI-MDI-QKD) protocol by introducing an advantage extraction technique when considering non-ideal factors such as detector post-pulse effect and finite sample statistical fluctuations.

[0007] To achieve the above objectives, the present invention provides a method for improving the performance of dual-independent quantum key distribution in a practical reference frame measurement device, comprising the following steps:

[0008] S1. Alice and Bob, the two communicating parties, each randomly select a light intensity and a local basis vector to prepare a quantum state. Then, Alice and Bob send the prepared quantum state to an untrusted third party, Charlie.

[0009] S2. Charlie, a third party, performs Bell state projection measurement on the received quantum state and announces the successful measurement event to Alice and Bob through a classical channel.

[0010] S3. After repeating steps S1 to S2 multiple times, Alice and Bob divide their data into sets with different basis vectors and different light intensities based on the basis vectors and light intensities used in the published successful Bell state projection event.

[0011] S4, Alice, and Bob calculated the corresponding count rate and bit error rate based on the data of different basis vectors and different light intensities shared by both parties; then, based on the decoy state method, Alice and Bob estimated the channel parameters of the single photon state.

[0012] S5, Alice, and Bob each divided their original keys into several... Key blocks of length 1 bit are represented as follows: and Then Alice selects a random bit. For each Bit-length key blocks Perform a bitwise XOR operation and transmit the result through a classical channel. Send to Bob; Bob receives the result. Then, calculate The result; if and only if Bob obtains the result is or At that time, Alice and Bob reserved the first bit of the key block, i.e. and , as the key after advantage extraction;

[0013] S6, Alice, and Bob perform key negotiation and post-processing for security enhancement based on the channel parameters of the single-photon state and the extracted key to extract the final secure key.

[0014] A further preferred embodiment of the present invention is that, in step S1, the communicating parties Alice and Bob each randomly select a light intensity and a local basis vector to prepare a quantum state; specifically:

[0015] Alice and Bob, the two communicating parties, each randomly select a light intensity. and a local basis To prepare quantum states, suppose Alice and Bob choose the light intensity The probabilities are respectively Select local basis vectors The probabilities are respectively subscript Represents the variable belonging to Alice or Bob; the prepared quantum state from Random selection from the list.

[0016] Preferably, in step S3, Alice and Bob divide their respective data into sets with different basis vectors and different light intensities based on the basis vectors and light intensities used in the published successful Bell state projection event, denoted as... ,in , representing different combinations of basis vectors.

[0017] Preferably, in step S4, Alice and Bob calculate the corresponding count rate based on the data of different light intensities and different basis vectors shared by both parties. and bit error rate ;

[0018] Then, based on the decoy state method, Alice and Bob estimated the channel parameters of the single-photon state, i.e., basis vector combination. Upper bound of single-photon state count rate and the lower realm Combination with basis vectors Upper bound of the bit error rate of the ordered photon state and the lower realm The calculation formula is:

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] Re-estimate the statistic The upper realm and the lower realm :

[0024] ;

[0025] .

[0026] Preferably, the final security key extracted in step S6 is represented as:

[0027] ;

[0028] The constraints are:

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] ,

[0034] ,

[0035] ,

[0036] ,

[0037] ,

[0038] ;

[0039] in, It is the Shannon binary entropy function; To improve error correction efficiency; Alice and Bob sent it at the same time. The probability that a signal pulse of high intensity contains a single-photon event; This represents the quantum channel characteristics controlled by Eve; for The lower bound of the single-photon count rate under the base; and for The upper and lower bounds of the bit error rate of a single photon under the given conditions; and These are statistics The upper and lower bounds; The length of the bit block divided using the advantage extraction method; It is the success rate of advantage extraction; for Total gain of signal states under the base; Before the implementation of advantage extraction Signal-state bit error rate under the base; It is the result of performance advantage extraction The bit error rate of the signal state under the base.

[0040] Beneficial Effects: This invention introduces an advantage extraction method to improve the system performance of RFI-MDI-QKD, which considers post-pulse effects and statistical fluctuation effects. This method can effectively improve the secure key rate and secure transmission distance of the RFI-MDI-QKD protocol without changing the optical hardware. This invention can provide valuable reference technology for the practical research of RFI-MDI-QKD systems. Attached Figure Description

[0041] Figure 1 This is the detection unit of the RFI-MDI-QKD system in Example 1.

[0042] Figure 2 For when The coding curves of the RFI-MDI-QKD system under different post-pulse rates are shown.

[0043] Figure 3 For when Scatter plot of optimal b values ​​at different afterpulse rates.

[0044] Figure 4 For when The coding curves of the RFI-MDI-QKD system under different post-pulse rates are shown.

[0045] Figure 5 when Scatter plot of optimal b values ​​at different afterpulse rates.

[0046] Figure 6 For when At 50 km, the security key rate of the RFI-MDI-QKD system under different afterpulse rates.

[0047] Figure 7 For when At 50 km, the security key rate of the RFI-MDI-QKD system under different code lengths. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, embodiments of this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. In the description of this invention, it should be understood that the terminology used is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0049] The following is combined Figures 1-7 This invention describes a method for improving the performance of dual-independent quantum key distribution in a real-reference frame measurement device.

[0050] Example: This example provides a method for improving the performance of dual-independent quantum key distribution in a real-reference frame measurement device.

[0051] Since RFI-MDI-QKD systems typically use single-photon avalanche detectors as the detection device, the actual afterpulse effect must be considered. To improve performance when considering non-ideal factors such as detector afterpulse effect and finite-sample statistical fluctuations, a dominance extraction technique is introduced into the reference frame measurement device dual-independent quantum key distribution (RFI-MDI-QKD) protocol. Specifically, the following steps are included:

[0052] S1. Quantum state preparation: Alice and Bob, the two communicating parties, each randomly select a light intensity and a local basis vector to prepare a quantum state. Then, Alice and Bob send the prepared quantum state to an untrusted third party, Charlie.

[0053] Alice and Bob, the two communicating parties, each randomly select a light intensity. and a local basis To prepare quantum states, suppose Alice and Bob choose the light intensity The probabilities are respectively Select local basis vectors The probabilities are respectively subscript Represents the variable belonging to Alice or Bob; the prepared quantum state from Random selection. Specifically:

[0054] In this embodiment, This indicates the light intensity combination chosen by Alice and Bob: .by The combination of encoded quantum states used to represent Alice and Bob: In combination In this table, the first symbol of each element represents Alice's strength (quantum state), and the second symbol represents Bob's strength (quantum state). For ease of understanding, this embodiment represents the encoded quantum states of Alice and Bob in the basis vectors of the computation table as follows: and Quantum states and coefficients encoded by Alice and Bob , The relationships between them are shown in Table 1. In Table 1, This represents Alice's (Bob's) local reference frame, and the relative deflection angle between Alice and Bob's reference frames. .

[0055] Table 1 Quantum states sent by Alice (Bob) and , Relationship

[0056]

[0057] Next, taking polarization encoding as an example, this embodiment details the evolution process of the quantum states prepared by Alice and Bob. Alice and Bob used a phase randomized light source to prepare... Intensity The quantum state is represented as:

[0058] ;

[0059] in, and For global random phase, and Let represent Alice's (Bob's) horizontal and vertical polarizations, respectively. The quantum state received by the detector is denoted as:

[0060] ;

[0061] in, , It refers to the detector's detection efficiency. The fiber loss factor is (dB / km). It is the distance between Alice (Bob) and Charlie.

[0062] Therefore, the average number of photons received by each detector is:

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] in, This indicates four detectors; This indicates the relative phase between Alice and Bob; ; ; ; ; When Alice and Bob were in intensity Encoding quantum states hour, The average response probability of the detector can be expressed as:

[0068] ;

[0069] in, This represents the dark count rate of the single-photon detector. Therefore, the average response probability under different light intensities... It can be represented as:

[0070] ;

[0071] in, Alice (Bob) sent a signal with a strength of The probability of; Is it when Alice (Bob)'s strength is At that time, Alice (Bob) sent a status The conditional probability. Considering the afterpulse effect, based on the non-Markovian property of the afterpulse in a single-photon detector, the afterpulse probability in a practical RFI-MDI-QKD system is... for

[0072] ;

[0073] in, Let be the total afterpulse rate. Therefore, considering the actual afterpulse effect, the response probabilities of the four detectors can be expressed as:

[0074] .

[0075] S2, Quantum State Measurement: Charlie, a third party, performs Bell projection measurement on the received quantum state and announces the successful measurement event to Alice and Bob through a classical channel.

[0076] In such Figure 1In a practical RFI-MDI-QKD system, the pulses transmitted by Alice and Bob interfere in Charlie's beam splitter (BS) and then pass through a polarization beam splitter (PBS). The horizontally polarized pulses arrive... or The detector receives vertically polarized pulses. or Detector. Only projected onto Bell state. and Events that meet the criteria are considered successful response events, while all other events are considered unsuccessful response events. For example... Figure 1 As shown, express and Simultaneous response or and Simultaneous response; express and Simultaneous response or and Simultaneous response. (Note) and Choose intensity for Alice and Bob and quantum state When the projection result is obtained and The probability of . After considering the after-pulse effect and integrating over the full-phase space, we can obtain:

[0077] ;

[0078] ;

[0079] in, It is a modified Bessel function of the first kind.

[0080] S3. Basis Setting: After Alice and Bob repeat steps S1 and S2 N times, they broadcast the basis vectors and light intensities used in the successful Bell state projection events. Based on the published basis vectors and light intensities, Alice and Bob divide their data into sets with different basis vectors and different light intensities, denoted as... ,in , representing different combinations of basis vectors.

[0081] S4. Parameter Estimation: Alice and Bob calculated the corresponding count rate based on the data of different basis vectors and different light intensities shared by both parties. and bit error rate Then, based on the decoy state method, Alice and Bob estimated the channel parameters of the single-photon state.

[0082] This embodiment uses Taking a base as an example, we give the expressions for its total gain and qubit error rate. Under this condition, the total gain of the actual RFI-MDI-QKD system is:

[0083] ;

[0084] The corresponding qubit error rate is:

[0085] ;

[0086] in, This is the baseline bit error rate; To disregard The bit error rate of a quantum bit at a given time can be expressed as:

[0087] ;

[0088] Similarly, when Alice and Bob choose other basis vector combinations to prepare the quantum state, the total gain and qubit error rate can be obtained using the same method. Thus, for a practical RFI-MDI-QKD system, a count rate and bit error rate model compatible with post-pulse effects can be established.

[0089] Furthermore, considering that Alice and Bob can only emit a limited number of light pulses in the actual RFI-MDI-QKD system, the statistical fluctuation deviation between the observed and expected values ​​under the limited number of pulses can be analyzed using the Chernov bound.

[0090] Assuming Alice and Bob send a total of N pulses, the following will continue with... This example illustrates how to estimate the channel parameters of a single-photon state. Alice chooses a light intensity of... And Bob chose a light intensity of hour, The total number of events in the response under the base is:

[0091] ;

[0092] Based on the analysis of statistical fluctuation effects, we can utilize... The upper and lower bounds of the corresponding expected value are derived from the sum of the number of events in the base response observed:

[0093] ;

[0094] ;

[0095] in and The value of can be obtained by solving the following formula:

[0096] ;

[0097] ;

[0098] Furthermore, after statistical fluctuation analysis, we can obtain... Upper and lower bounds:

[0099] ;

[0100] .

[0101] S5, Advantage Extraction:

[0102] Alice and Bob divided their respective original keys into several... Key blocks of length 1 bit are represented as follows: and Then Alice selects a random bit. For each Bit-length key blocks Perform a bitwise XOR operation and transmit the result through a classical channel. Send to Bob; Bob receives the result. Then, calculate The result; if and only if Bob obtains the result is or At that time, Alice and Bob reserved the first bit of the key block, i.e. and , as the key after advantage extraction;

[0103] S6. Post-processing: Based on the channel parameters of the single-photon state and the extracted key, Alice and Bob perform post-processing for key negotiation and confidentiality enhancement to extract the final secure key.

[0104] The final extracted security key is represented as:

[0105] ;

[0106] The constraints are:

[0107] ,

[0108] ,

[0109] ,

[0110] ,

[0111] ,

[0112] ,

[0113] ,

[0114] ,

[0115] ,

[0116] ;

[0117] in, It is the Shannon binary entropy function; To improve error correction efficiency; Alice and Bob sent it at the same time. The probability that a signal pulse of high intensity contains a single-photon event; This represents the quantum channel characteristics controlled by Eve; for The lower bound of the single-photon count rate under the base; and for The upper and lower bounds of the bit error rate of a single photon under the given conditions; and These are statistics The upper and lower bounds; The length of the bit block divided using the advantage extraction method; It is the success rate of advantage extraction; for Total gain of signal states under the base; Before the implementation of advantage extraction Signal-state bit error rate under the base; It is the result of performance advantage extraction The bit error rate of the signal state under the base.

[0118] The performance of the RFI-MDI-QKD protocol in this embodiment is then simulated and verified.

[0119] The core parameter of the simulation is the detector's detection efficiency. Dark count rate Error correction efficiency The loss factor of a standard optical fiber communication link is: The safety factor for statistical fluctuations using the Chernov bound method is: . Figures 2-7 The results are from the simulation.

[0120] Figure 2 For when The figure shows the coding curves of the RFI-MDI-QKD system under different afterpulse rates. The solid and dashed lines in the figure represent the coding curves when the afterpulse probability is different. Secure key rates with and without the advantage extraction method at 1% and 1.5%.

[0121] Figure 3 For when Scatter plot of optimal b values ​​under different afterpulse rates. The purple diamonds and green circles in the plot represent the afterpulse probabilities, respectively. The optimal b values ​​are 1% and 1.5%.

[0122] Figure 4 For when The graph shows the coding curves of the RFI-MDI-QKD system under different afterpulse rates. The solid and dashed lines in the graph, from top to bottom, represent the coding curves when the afterpulse probability is different. Secure key rates with and without the advantage extraction method at 1% and 1.5%.

[0123] Figure 5 when Scatter plot of optimal b values ​​for different afterpulse rates. The purple diamonds and green circles in the plot represent afterpulse probabilities. The optimal b values ​​are 1% and 1.5%.

[0124] Figure 6 For when At a distance of 50 km, the security key rates of the RFI-MDI-QKD system under different afterpulse rates are shown. The data points marked with green squares, red circles, and blue triangles represent the security key rates for block bit lengths of 1, 2, and 3, respectively.

[0125] Figure 7 For when At a distance of 50 km, the security key rates of the RFI-MDI-QKD system under different code lengths are shown. The data points marked with red squares, green circles, and purple triangles represent the security key rates when the block bit length is 1, 2, and 3, respectively.

[0126] Simulation results show that, considering the after-pulse effect and statistical fluctuation effect, the advantage extraction method can effectively improve the secure key rate and secure transmission distance of the RFI-MDI-QKD protocol without changing the optical hardware.

[0127] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to 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 dual-independent quantum key distribution in a practical reference frame measurement device, characterized in that, Includes the following steps: S1. Alice and Bob, the two communicating parties, each randomly select a light intensity and a local basis vector to prepare a quantum state. Then, Alice and Bob send the prepared quantum state to an untrusted third party, Charlie. S2. Charlie, a third party, performs Bell state projection measurement on the received quantum state and announces the successful measurement event to Alice and Bob through a classical channel. S3. After repeating steps S1 to S2 multiple times, Alice and Bob divide their data into sets with different basis vectors and different light intensities based on the basis vectors and light intensities used in the published successful Bell state projection event. S4, Alice, and Bob calculated the corresponding count rate and bit error rate based on the data of different basis vectors and different light intensities shared by both parties; then, based on the decoy state method, Alice and Bob estimated the channel parameters of the single photon state. S5, Alice, and Bob each divided their original keys into several... Key blocks of length 1 bit are represented as follows: and Then Alice selects a random bit. For each Bit-length key blocks Perform a bitwise XOR operation and transmit the result through a classical channel. Send to Bob; Bob receives the result. Then, calculate The result; if and only if Bob obtains the result is or At that time, Alice and Bob reserved the first bit of the key block, i.e. and , as the key after advantage extraction; S6, Alice, and Bob perform key negotiation and post-processing for security enhancement based on the channel parameters of the single-photon state and the extracted key to extract the final secure key.

2. The method for improving the performance of dual-independent quantum key distribution in a real reference frame measurement device according to claim 1, characterized in that, In step S1, Alice and Bob, the two communicating parties, each randomly select a light intensity and a local basis vector to prepare the quantum state; specifically: Alice and Bob, the two communicating parties, each randomly select a light intensity. and a local basis To prepare quantum states, suppose Alice and Bob choose the light intensity The probabilities are respectively Select local basis vectors The probabilities are respectively subscript Represents the variable belonging to Alice or Bob; the prepared quantum state from Random selection from the list.

3. The method for improving the performance of dual-independent quantum key distribution in a real reference frame measurement device according to claim 2, characterized in that, In step S3, Alice and Bob, based on the basis vectors and light intensities used in the successfully published Bell state projection event, divide their respective data into sets with different basis vectors and different light intensities, represented as follows: ,in , representing different combinations of basis vectors.

4. The method for improving the performance of dual-independent quantum key distribution in a real reference frame measurement device according to claim 3, characterized in that, In step S4, Alice and Bob calculate the corresponding count rate based on the data of different light intensities and different basis vectors shared by both parties. and bit error rate ; Then, based on the decoy state method, Alice and Bob estimated the channel parameters of the single-photon state, i.e., basis vector combination. Upper bound of single-photon state count rate and the lower realm Combination with basis vectors Upper bound of the bit error rate of the ordered photon state and the lower realm The calculation formula is: ； ； ； ； Re-estimate the statistic The upper realm and the lower realm : ； 。 5. The method for improving the performance of dual-independent quantum key distribution in a real reference frame measurement device according to claim 1, characterized in that, The final security key extracted in step S6 is represented as: ； The constraints are: ， ， ， ， ， ， ， ， ， ； in, It is the Shannon binary entropy function; To improve error correction efficiency; Alice and Bob sent it at the same time. The probability that a signal pulse of high intensity contains a single-photon event; This represents the quantum channel characteristics controlled by Eve; for The lower bound of the single-photon count rate under the base; and for The upper and lower bounds of the bit error rate of a single photon under the given conditions; and These are statistics The upper and lower bounds; The length of the bit block divided using the advantage extraction method; It is the success rate of advantage extraction; for Total gain of signal states under the base; Before the implementation of advantage extraction Signal-state bit error rate under the base; It is the result of performance advantage extraction The bit error rate of the signal state under the base.

Images