Continuous variable quantum secret sharing method based on state distinguishing detector

Abstract

The invention discloses a continuous variable quantum secret sharing method based on a state distinguishing detector. The method comprises the following steps: a user generates a binary key sequence; a QPSK state signal is generated; sequentially coupling the QPSK state signals through an asymmetric beam splitter; the Dealer uses the SDD to estimate the received signal; repeating the steps, and extracting an original combined key; obtaining an original key of each user based on a key sequence combination principle; and calculating a key rate, and extracting a key to complete encryption message decoding. According to the method, quantum state distinguishing is completed through a state distinguishing detector (SDD), and the SDD is allowed to directly determine bit information directly transmitted by different users by identifying mixed state categories, so that each user does not need to declare and discard respective original key subsets, a mapping rule is directly restored, key loss is reduced, and the user experience is improved. And the key rate performance of the SDD-CVQSS protocol is improved. In addition, compared with the traditional CVQSS, the SDD-CVQSS shows obvious advantages in key performance indexes of the key rate and the maximum transmission distance.

Description

Technical Field

[0001] This invention belongs to the field of quantum communication technology, specifically relating to a continuous variable quantum secret sharing method based on a state distinguishing detector. Background Technology

[0002] Secret sharing (SS) aims to provide multiple keys to a group of remote users. In a typical... In the threshold scheme, the secret is divided into Only by possessing at least one of them can one obtain a share. Only with sufficient data can it be fully reconstructed. With the rapid development of quantum technology, quantum secret sharing (QSS) has been proposed. Its security is no longer based on computational complexity but is guaranteed by the laws of quantum mechanics, thus raising the theoretical security level from computational security to unconditional security. Subsequently, QSS was extended to the continuous variable domain (CVQSS), where the key bits are usually encoded on the canonical components of the optical field, offering advantages such as low detection cost, high theoretical security code rate, and ease of integration. CVQSS using weakly coherent states involves each participant injecting locally prepared coherent states into a cyclic optical mode. Its preparation is simple and it is well compatible with modern optical communication networks.

[0003] In the actual implementation of CVQSS, the detection error rate of traditional coherent detectors has been proven to be unable to break through the standard quantum limit (SQL), and a secret sharing link with the receiver Dealer must be completed by the user publishing part of the original key. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a continuous variable quantum secret sharing method based on a state-discriminating detector (SDD). The SDD achieves quantum state discrimination, allowing the SDD to directly determine the bit information transmitted directly by different users by identifying mixed state categories. This eliminates the need for each user to declare and discard their own original key subset, directly restoring the mapping rules, reducing key loss, and improving the key rate performance of the SDD-CVQSS protocol.

[0005] This invention provides a continuous variable quantum secret sharing method based on a state-discriminating detector, comprising the following steps:

[0006] S1. Sort a number of remote users from farthest to nearest in order of their distance from the Dealer. The remote user is connected to the Dealer in a sorted manner via an untrusted quantum channel;

[0007] S2. For each quantum transmission, all remote users first randomly generate a binary key sequence, divide it into pairs and map it onto four coherent states to prepare a QPSK state;

[0008] S3. The prepared QPSK state Send to , Prepared QPSK state Coupled to via a highly asymmetric beam splitter The prepared input signal state is in the same pattern as the QPSK state, and then compared with the prepared QPSK state. Mixed sent to ;

[0009] S4. Following the method in step S3, according to the remote user The signals are sorted and mixed sequentially to obtain a final mixed signal. Mixed signals Send to Dealer;

[0010] S5. Dealer receives mixed signals. Then, a state-discriminating detector is used, and the maximum a posteriori probability criterion is employed to estimate the received signal. After each estimation, the result is used as the displacement gate parameter for the next adaptive measurement. This process is repeated until the final estimation result is obtained after M adaptive measurements. ;

[0011] S6. Repeat steps S2 to S5 until the Dealer obtains a preset number of estimation results, and then maps all estimation results to the original binary sequence according to the mapping rules to extract the original combined key set;

[0012] S7. Based on the original combined key set, the Dealer obtains the original keys of all remote users according to the key sequence combination principle;

[0013] S8. The Dealer establishes contact with remote users based on the original key, obtains the estimated key rate by calculating the information entropy and von Neumann entropy, and then performs sequence execution error correction negotiation and secret amplification on the remote users respectively to extract the keys of all remote users.

[0014] S9. The Dealer obtains the final key based on the keys of all remote users, encodes the message using the final key, and publishes the encoded message to all remote users, thus completing the quantum secret sharing.

[0015] In step S2, the length of the binary key sequence is n; the QPSK state is represented by the following formula: ;in, Number the coherent state category; The imaginary unit; The coherence amplitude is represented by j; the remote user number is represented by j.

[0016] Step S2 specifically involves: For any remote user j, first generate an m-bit binary sequence. Then the binary sequence Divide into pairs and map them to four coherent states according to the following mapping rules: ;

[0017] In step S4, the mixed signal Express it using the following formula: ;in, for The channel transmittance experienced by the signal between the dealer and the channel. for The channel transmittance experienced by the signal between the dealer and the channel. for The channel transmittance experienced by the signal between the signal and the dealer; k is the mixed state category;

[0018] Step S5 is as follows:

[0019] Use a beam splitter to mix the signals. Divided into M equal-intensity portions, the reflectivities of the M beam splitters are respectively ;in, Here, M is the index of the branch, and M is the total number of branches; the signal for each branch is... ;

[0020] For the m-th adaptive strategy, the transmittance is used. The parameter optical signal on the beam splitter is unique, and the parameter optical coherence amplitude is set to... The signal obtained after displacement is: ;in, The amplitude parameter of the beam splitter interference light during the i-th round of adaptive measurement;

[0021] Introducing the thermal noise caused by the temperature-induced resistance of the continuous working load (SDD), the signal density operator after displacement is expressed by the following formula: ;in, The average number of thermal photons; For the entire complex plane; To receive the eigenvalues ​​of the coherent state;

[0022] The unique state is measured using a photon number-resolved detector, and the quantum mechanical description is expressed in the form of a positive operator value measurement, using the following formula: in, The quantum efficiency of a photon number-resolved detector; is the number of probe photons on the i-th branch; j is the actual number of incident photons.

[0023] The conditional probability of detecting a photon number on a photon number-resolved detector is calculated using the following formula: ;in, for Laguerre polynomial of order 1; The average photon number is calculated using the following formula: ;in, The visibility of the interference is M; M is the total number of branches.

[0024] After the measurement is completed, based on the current detection history and displacement history Using Bayesian inference, the posterior probabilities of all possible states can be obtained; for the ... Each possible state in the sub-adaptive measurement Its posterior probability Calculate using the following formula: in, For the first The posterior probability in subadaptive measurement; according to the maximum a posteriori (MAP) criterion, the possible state with the highest posterior probability is... Using this as the input hypothesis for the next adaptive measurement, the posterior probability of the state will become the prior probability of the state in the next adaptive measurement, and the latest measurement result and the state selected in the adaptive measurement will be added to the history respectively. and middle;

[0025] The posterior probability of each possible state after M adaptive measurements is expressed by the following formula: in, The number of photons measured in phase 0; This is the prior probability;

[0026] Final estimated state The state with the highest posterior probability in M ​​adaptive measurements. ;in, The amplitude parameters of the interference light of the beam splitter in stage 0.

[0027] In step S7, the original combined key set is represented by the following formula: Where L is the original set of combined keys; The first information bit; n is the total number of users; m is the total number of bits sent by a single user;

[0028] Based on the principle of key sequence combination, we obtain raw key It can be expressed using the following formula: in, , This is the floor symbol.

[0029] In step S9, the final key is ;in, The key for remote user i;

[0030] The message M is then encoded using the final key, represented by the following formula: Where E represents the encoded message;

[0031] The encoded message E is announced to all remote users. Only when all remote users combine their shares is the message E correctly decoded, thus completing the quantum secret sharing.

[0032] This invention discloses a continuous-variable quantum secret sharing method based on a state-discriminating detector (SDD). The SDD achieves quantum state discrimination, allowing it to directly determine the bit information transmitted by different users by identifying mixed state categories. This eliminates the need for each user to declare and discard their original key subset, directly restoring the mapping rules, reducing key loss, and improving the key rate performance of the SDD-CVQSS protocol. Furthermore, compared to traditional CVQSS, SDD-CVQSS demonstrates significant advantages in key performance indicators such as key rate and maximum transmission distance. Attached Figure Description

[0033] Figure 1 This is a schematic flowchart of the method of the present invention;

[0034] Figure 2 This is a schematic diagram of the SDD detection process in the method of the present invention;

[0035] Figure 3 These are the error probability curves of the State Differentiation Detector (SDD) under different conditions in embodiments of the present invention.

[0036] Figure 4 This is a schematic diagram of the security model in an embodiment of the present invention;

[0037] Figure 5 This is a schematic diagram of the signal modulation strategy process under two user scenarios in an embodiment of the present invention;

[0038] Figure 6 This is a schematic diagram of the performance test results in an embodiment of the present invention. Detailed Implementation

[0039] This invention provides a continuous variable quantum secret sharing method based on a state-discriminating detector, the flowchart of which is shown below. Figure 1 As shown, it includes the following steps:

[0040] S1. Sort a number of remote users from farthest to nearest in order of their distance from the Dealer. The remote user is connected to the Dealer in a sorted manner via an untrusted quantum channel;

[0041] S2. For each quantum transmission, all remote users first randomly generate a binary key sequence, divide it into pairs and map it onto four coherent states to prepare a QPSK state;

[0042] In step S2, the length of the binary key sequence is n; the QPSK state is represented by the following formula: ;in, Number the coherent state category; The imaginary unit; The coherence amplitude is represented by j; the remote user number is represented by j.

[0043] Step S2 specifically involves: For any remote user j, first generate an m-bit binary sequence. Then the binary sequence Divide into pairs and map them to four coherent states according to the following mapping rules: ;

[0044] S3. The prepared QPSK state Send to , Prepared QPSK state Coupled to via a highly asymmetric beam splitter The prepared input signal state is in the same pattern as the QPSK state, and then compared with the prepared QPSK state. Mixed sent to ;

[0045] S4. Following the method in step S3, according to the remote user The signals are sorted and mixed sequentially to obtain a final mixed signal. Mixed signals Send to Dealer;

[0046] In step S4, the mixed signal Express it using the following formula: ;in, for The channel transmittance experienced by the signal between the dealer and the channel. for The channel transmittance experienced by the signal between the dealer and the channel. for The channel transmittance experienced by the signal between the signal and the dealer; k is the mixed state category;

[0047] S5. Dealer receives mixed signals. Then, a state-discriminating detector is used, and the maximum a posteriori probability criterion is employed to estimate the received signal. After each estimation, the result is used as the displacement gate parameter for the next adaptive measurement. This process is repeated until the final estimation result is obtained after M adaptive measurements. The flow chart of the SDD detection process is shown below. Figure 2 As shown;

[0048] Step S5 is as follows:

[0049] Use a beam splitter to mix the signals. Divided into M equal-intensity portions, the reflectivities of the M beam splitters are respectively ;in, Here, M is the index of the branch, and M is the total number of branches; the signal for each branch is... ;

[0050] For the m-th adaptive strategy, the transmittance is used. The parameter optical signal on the beam splitter is unique, and the parameter optical coherence amplitude is set to... The signal obtained after displacement is: ;in, The amplitude parameter of the beam splitter interference light during the i-th round of adaptive measurement;

[0051] Introducing the thermal noise caused by the temperature-induced resistance of the continuous working load (SDD), the signal density operator after displacement is expressed by the following formula: ;in, The average number of thermal photons; For the entire complex plane; To receive the eigenvalues ​​of the coherent state;

[0052] The unique state is measured using a photon number-resolved detector, and the quantum mechanical description is expressed in the form of a positive operator value measurement, using the following formula: in, The quantum efficiency of a photon number-resolved detector; is the number of probe photons on the i-th branch; j is the actual number of incident photons.

[0053] The conditional probability of detecting a photon number on a photon number-resolved detector is calculated using the following formula: ;in, for Laguerre polynomial of order 1; The average photon number is calculated using the following formula: ;in, The visibility of the interference is M; M is the total number of branches.

[0054] After the measurement is completed, based on the current detection history and displacement history Using Bayesian inference, the posterior probabilities of all possible states can be obtained; for the ... Each possible state in the sub-adaptive measurement Its posterior probability Calculate using the following formula: in, For the first The posterior probability in subadaptive measurement; according to the maximum a posteriori (MAP) criterion, the possible state with the highest posterior probability is... Using this as the input hypothesis for the next adaptive measurement, the posterior probability of the state will become the prior probability of the state in the next adaptive measurement, and the latest measurement result and the state selected in the adaptive measurement will be added to the history respectively. and middle;

[0055] The posterior probability of each possible state after M adaptive measurements is expressed by the following formula: in, The number of photons measured in phase 0; This is the prior probability;

[0056] Final estimated state The state with the highest posterior probability in M ​​adaptive measurements. ;in, The amplitude parameters of the interference light of the beam splitter in stage 0.

[0057] Given the average error probability of the adaptive receiver: ;

[0058] Based on this average probability, the error probability curves of the state discrimination detector (SDD) under different conditions can be obtained as follows: Figure 3 As shown.

[0059] S6. Repeat steps S2 to S5 until the Dealer obtains a preset number of estimation results, and then maps all estimation results to the original binary sequence according to the mapping rules to extract the original combined key set;

[0060] S7. Based on the original combined key set, the Dealer obtains the original keys of all remote users according to the key sequence combination principle;

[0061] In step S7, the original combined key set is represented by the following formula: Where L is the original set of combined keys; The first information bit; n is the total number of users; m is the total number of bits sent by a single user;

[0062] Based on the principle of key sequence combination, we obtain raw key It can be expressed using the following formula: in, , This is the floor symbol.

[0063] S8. The Dealer establishes contact with remote users based on the original key, obtains the estimated key rate by calculating the information entropy and von Neumann entropy, and then performs sequence execution error correction negotiation and secret amplification on the remote users respectively to extract the keys of all remote users.

[0064] S9. The Dealer obtains the final key based on the keys of all remote users, encodes the message using the final key, and publishes the encoded message to all remote users, thus completing the quantum secret sharing.

[0065] In step S9, the final key is ;in, The key for remote user i;

[0066] The message M is then encoded using the final key, represented by the following formula: Where E represents the encoded message;

[0067] The encoded message E is announced to all remote users. Only when all remote users combine their shares is the message E correctly decoded, thus completing the quantum secret sharing.

[0068] A security model is established for the method of this invention, such as... Figure 4 As shown, the details are as follows:

[0069] Taking a user base of 2 as an example, user 1 first prepares QMCSs and sends them to user 2. User 2 also independently prepares QMCSs using the same QPSK modulation strategy. Therefore, the mixed state at the output of user 2 can be represented as follows: By treating User 1 and User 2 as a single sender, the SDD-CVQSS security model can be viewed as a point-to-point communication link, employing... Figure 5 The 16QAM-like modulation strategy is shown. Assuming the quantum channel between the sender and receiver is a photon-loss channel, the eavesdropper Eve applies a beam splitting collective attack to obtain information about the key, splitting the mixture state into...

[0070] This splitting process reflects the information leakage caused by the Eve attack, including the state. Received by Dealer, status Received by Eve. Then, the received state is estimated using SDD. Finally, the estimated state is obtained after adaptive measurement. .

[0071] This model provides the maximum amount of information Eve can acquire under collective beam splitting attacks, thus providing a reliable security guarantee for the protocol.

[0072] Finally, regarding the method of this invention, noise and device defects are used as influencing parameters through numerical simulation, including detection efficiency. Thermal noise Imperfect visible light interference Dark counting noise and the transmittance of the beam splitter Based on the above, the asymptotic key rate of SDD-CVQSS was evaluated. Performance graphs are shown below. Figure 6 As shown.

[0073] Figure 6 The asymptotic performance of SDD-CVQSS with four-round adaptive measurement is shown. For comparison, the asymptotic performance of traditional CVQSS and SDD-CVQK is also plotted. It can be seen that our proposed SDD-CVQSS with reverse negotiation (RR) (solid red line) significantly outperforms all other schemes in terms of maximum transmission distance and key rate, even exceeding the Priandola-Laurenza-Ottaviani-Banchi (PLOB) limit (dashed purple line) at a transmission distance of 14.71 km. This improvement is mainly attributed to two aspects: the data coordination strategy and the deployment of SDD. Specifically, for the data coordination strategy, RR has been shown to outperform forward negotiation (DR) limited to 3dB. This is why the maximum transmission distance of SDD-CVQSS with RR (solid red line) is better than that of the DR version (dashed yellow line). For the deployment of SDD, by comparing SDD-CVQSS with RR (red solid line) and traditional CVQSS with RR (green solid line), the advantages of SDD in improving CVQSS key rate can be clearly reflected, thus illustrating the significant advantage of SDD in improving CVQSS key rate.

Claims

1. A continuous-variable quantum secret sharing method based on a state-discriminating detector, characterized in that, Includes the following steps: S1. Sort a number of remote users from farthest to nearest in order of their distance from the Dealer. The remote user is connected to the Dealer in a sorted manner via an untrusted quantum channel; S2. For each quantum transmission, all remote users first randomly generate a binary key sequence, divide it into pairs and map it onto four coherent states to prepare a QPSK state; S3. The prepared QPSK state Send to , Prepared QPSK state Coupled to via a highly asymmetric beam splitter The prepared input signal state is the same as the pattern, and then... The prepared QPSK state Mixed sent to ; S4. Following the method in step S3, according to the remote user The signals are sorted and mixed sequentially to obtain a final mixed signal. Mixed signals Send to Dealer; S5. Dealer receives mixed signals. Then, a state-discriminating detector is used, and the maximum a posteriori probability criterion is employed to estimate the received signal. After each estimation, the result is used as the displacement gate parameter for the next adaptive measurement. This process is repeated until the final estimation result is obtained after M adaptive measurements. ; S6. Repeat steps S2 to S5 until the Dealer obtains a preset number of estimation results, and then maps all estimation results to the original binary sequence according to the mapping rules to extract the original combined key set; S7. Based on the original combined key set, the Dealer obtains the original keys of all remote users according to the key sequence combination principle; S8. The Dealer establishes contact with remote users based on the original key, obtains the estimated key rate by calculating the information entropy and von Neumann entropy, and then performs sequence execution error correction negotiation and secret amplification on the remote users respectively to extract the keys of all remote users. S9. The Dealer obtains the final key based on the keys of all remote users, encodes the message using the final key, and publishes the encoded message to all remote users, thus completing the quantum secret sharing.

2. The continuous variable quantum secret sharing method based on a state-discriminating detector according to claim 1, characterized in that, In step S2, the length of the binary key sequence is n; the QPSK state is represented by the following formula: ;in, Number the coherent state category; The imaginary unit; is the coherence amplitude; j is the remote user sequence number.

3. The continuous variable quantum secret sharing method based on a state-discriminating detector according to claim 2, characterized in that, Step S2 specifically involves: For any remote user j, first generate an m-bit binary sequence. Then the binary sequence Divide into pairs and map them to four coherent states according to the following mapping rules: .

4. The continuous variable quantum secret sharing method based on a state-discriminating detector according to claim 1, characterized in that, In step S4, the mixed signal Express it using the following formula: ;in, for The channel transmittance experienced by the signal between the dealer and the channel. for The channel transmittance experienced by the signal between the dealer and the channel. for The channel transmittance experienced by the signal between the Dealer and the Dealer; k is the mixed state category.

5. The continuous variable quantum secret sharing method based on a state-discriminating detector according to claim 1, characterized in that, In step S5, a beam splitter is used to split the mixed signal. Divided into M equal-intensity portions, the reflectivities of the M beam splitters are respectively ;in, Here, M is the index of the branch, and M is the total number of branches; the signal for each branch is... ; For the m-th adaptive strategy, the transmittance is used. The parameter optical signal on the beam splitter is unique, and the parameter optical coherence amplitude is set to... The signal obtained after displacement is: ;in, The amplitude parameter of the beam splitter interference light during the i-th round of adaptive measurement.

6. The continuous variable quantum secret sharing method based on a state-discriminating detector according to claim 5, characterized in that, In step S5, the SDD is introduced to address the thermal noise caused by the temperature-induced complex resistance of the working resistor. The signal density operator after displacement is expressed by the following formula: ;in, The average number of thermal photons; For the entire complex plane; To receive the eigenvalues ​​of the coherent state; The unique state is measured using a photon number-resolved detector, and the quantum mechanical description is expressed in the form of a positive operator value measurement, using the following formula: in, The quantum efficiency of a photon number-resolved detector; is the number of probe photons on the i-th branch; j is the actual number of incident photons. The conditional probability of detecting a photon number on a photon number-resolved detector is calculated using the following formula: ;in, for Laguerre polynomial of order 1; The average photon number is calculated using the following formula: ;in, The visibility of the interference is M; M is the total number of branches. After the measurement is completed, based on the current detection history and displacement history We use Bayesian inference to obtain the posterior probabilities of all possible states; for the ... Each possible state in the sub-adaptive measurement Its posterior probability Calculate using the following formula: in, For the first The posterior probability in subadaptive measurement; according to the maximum a posteriori (MAP) criterion, the possible state with the highest posterior probability is... Using this as the input hypothesis for the next adaptive measurement, the posterior probability of the state will become the prior probability of the state in the next adaptive measurement, and the latest measurement result and the state selected in the adaptive measurement will be added to the history respectively. and middle.

7. The continuous variable quantum secret sharing method based on a state-discriminating detector according to claim 6, characterized in that, In step S5, the posterior probability of each possible state after M adaptive measurements is represented by the following formula: in, The number of photons measured in phase 0; This is the prior probability; Final estimated state The state with the highest posterior probability in M ​​adaptive measurements. ;in, The amplitude parameters of the interference light of the beam splitter in stage 0.

8. The continuous variable quantum secret sharing method based on a state-discriminating detector according to claim 1, characterized in that, In step S7, the original combined key set is represented by the following formula: Where L is the original set of combined keys; The first information bit; n is the total number of users; m is the total number of bits sent by a single user; Based on the principle of key sequence combination, we obtain raw key It can be expressed using the following formula: in, , This is the floor symbol.

9. The continuous variable quantum secret sharing method based on a state-discriminating detector according to claim 1, characterized in that, In step S9, the final key is ;in, The key for remote user i; The message M is then encoded using the final key, represented by the following formula: Where E represents the encoded message; The encoded message E is announced to all remote users. Only when all remote users combine their shares is the message E correctly decoded, thus completing the quantum secret sharing.

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