Semi-quantum key distribution network construction method based on single photons with polarization and empty mode freedom degrees

Abstract

The invention provides a semi-quantum key distribution network construction method based on single photons with polarization and empty mode freedom degrees, and aims that a participant with complete quantum capability establishes different keys with each semi-quantum participant, and at the same time, every two adjacent semi-quantum participants are helped to establish different keys are fulfilled. According to the method, only single photons instead of quantum entangled states are used as quantum resources, and only single photon measurement is needed. According to the method, key pre-sharing, quantum entanglement swap operation, quantum delay line operation and Hadamard operation are not needed. According to the method, external attacks of external eavesdroppers and internal attacks of participants can be effectively prevented. The method can be applied to semi-quantum summation, semi-quantum privacy comparison and semi-quantum secret sharing. Due to the fact that the single photons with polarization and empty mode freedom degrees are prepared, operation of measuring and applying unitary is easy to achieve technically, and the method has good practical feasibility.

Description

Technical Field

[0001] The present invention relates to the field of quantum cryptography. The present invention proposes a method for constructing a semi-quantum key distribution network based on single photons with polarization and empty mode freedom, achieving the goal of "a participant with full quantum capability establishes different keys with each semi-quantum participant, while helping every two adjacent semi-quantum participants to establish different keys". Background Art

[0002] In the information age, data monitoring and theft incidents occur frequently, posing a huge threat to personal privacy, financial security, national security, etc. Therefore, data security has become an extremely important issue. Traditional classical encryption algorithms based on computational complexity have always been an important cornerstone for protecting data information security, but with the rise and development of quantum computing technology, these algorithms are increasingly facing severe challenges. Therefore, there is an urgent need to find another safe and effective data protection method. In 1984, Bennett and Brassard [1] The first quantum key distribution (QKD) method, the famous BB84 method, was proposed, marking the birth of quantum cryptography. The function of QKD is to use the laws of quantum mechanics to establish a key between two remote users. So far, with the continuous advancement of quantum technology, many excellent QKD methods have been [2-8] QKD is expected to become one of the core technologies for data protection in the future.

[0003] Quantum cryptography methods, including QKD, often require all users to have full quantum capabilities, including the ability to prepare quantum superposition and quantum entanglement, the ability to measure quantum superposition and quantum entanglement, and the ability to perform unitary operations. This will undoubtedly make all users bear a heavy burden on quantum devices. In order to reduce the burden of quantum devices for some users, Boyer et al. [9,10] He was the first to propose the concept of "semi-quantum" and designed the first two semi-quantum key distribution (SQKD) methods, which marked the birth of semi-quantum cryptography. [9-21] Designed from different perspectives. According to the number of users, SQKD can be further divided into two-party semiquantum key distribution (TSQKD) [9-16] and Multi-party Semiquantum Key Distribution (MSQKD) [17-21]Currently, there are only a few MSQKD methods in the literature [17-21]. Zhang et al.

[17] In 2009, a novel MSQKD method was proposed, which realized the function of "a quantum participant and a group of semi-quantum participants jointly establish the same key"; Zhou et al.

[18] In 2019, a novel MSQKD method was proposed, which realized the function of "a quantum participant and two groups of semi-quantum participants establish different keys"; Tian et al.

[19] The MSQKD method proposed in 2022 has the function of "a quantum participant and a group of semi-quantum participants working together to establish the same key"; Pan

[20] The MSQKD method proposed in 2024 has the function of "a quantum participant establishing a different key with each semi-quantum participant"; Tsai and Wang

[21] The MSQKD method proposed in 2024 has the function of "a quantum participant helps a semi-quantum participant to establish the same key with a group of other semi-quantum participants". [17-21] They only have a single function and may not be applicable in more complex topological network structures.

[0004] In view of the above analysis, in order to realize the function of "a participant with full quantum ability establishes different keys with each half-quantum participant, and at the same time helps every two adjacent half-quantum participants to establish different keys", the present invention proposes a novel method for constructing a half-quantum key distribution network using single photons with polarization and empty mode degrees of freedom. The method of the present invention only requires single photons as quantum resources and only requires single photon measurements. The method of the present invention does not require the use of pre-shared keys, quantum entanglement exchange operations, quantum delay lines, and Hadamard operations. The method of the present invention can be applied to half-quantum summation, half-quantum privacy comparison, and half-quantum secret sharing.

[0005] References

[0006] [1]Bennett, CH, & Brassard, G. (1984). Quantum cryptography: Public keydistribution and coin tossing. Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, IEEE Press, 175-179.

[0007] [2]Ekert,A.K.(1991).Quantum cryptography based on Bell'stheorem.Physical Review Letters,67(6),661-663.

[0008] [3]Bennett,C.H.(1992).Quantum cryptography using any twononorthogonal states.Physical Review Letters,68(21),3121.

[0009] [4]Cabello,A.(2000).Quantum key distribution in the Holevolimit.Physical Review Letters,85(26),5635.

[0010] [5]Hwang,W.Y.(2003).Quantum key distribution with high loss:Towardglobal secure communication.Physical Review Letters,91(5),057901.

[0011] [6]Li,X.H.,Deng,F.G.,&Zhou,H.Y.(2008).Efficient quantum keydistribution over a collective noise channel.Physical Review A,78(2),022321.

[0012] [7]Zhang,C.M.,Song,X.T.,Treeviriyanupab,P.,Li,M.,Wang,C.,Li,H.W.,Yin,Z.Q.,Chen,W.,&Han,Z.F.(2014).Delayed error verification in quantum keydistribution.Chinese Science Bulletin,23(59),2825-2828.

[0013] [8]Scarni,V.(2004).Quantum cryptography protocols robust againstphoton number splitting attacks for weak laser pulse implementations.PhysicalReview Letters,92(5),579-582.

[0014] [9]Boyer,M.,Kenigsberg,D.,&Mor,T.(2007).Quantum key distribution withclassical Bob.Physical Review Letters,99(14),140501.

[0015]

[10] Boyer,M.,Gelles,R.,Kenigsberg,D.,&Mor,T.(2009).Semiquantum keydistribution.Physical Review A,79(3),032341.

[0016]

[11] Zou,X.,Qiu,D.,Li,L.,Wu,L.,&Li,L.(2009).Semiquantum-keydistribution using less than four quantum states.Physical Review A-Atomic,Molecular,and Optical Physics,79(5),052312.

[0017]

[12] Wang,J.,Zhang,S.,Zhang,Q.,&Tang,C.J.(2011).Semiquantum keydistribution using entangled states.Chinese Physics Letters,28(10),100301.

[0018]

[13] Zou,X.,Qiu,D.,Zhang,S.,&Mateus,P.(2015).Semiquantum keydistribution without invoking the classical party’s measurementcapability.Quantum Information Processing,14,2981-2996.

[0019]

[14] Ye,T.Y.,Li,H.K.,&Hu,J.L.(2020).Semi-quantum key distribution withsingle photons in both polarization and spatial-mode degrees offreedom.International Journal of Theoretical Physics,59(9),2807-2815.

[0020]

[15] Ye,T.Y.,Geng,M.J.,Xu,T.J.,&Chen,Y.(2022).Efficient semiquantumkey distribution based on single photons in both polarization and spatial-mode degrees of freedom.Quantum Information Processing,21(4),123.

[0021]

[16] Xu,T.J.,&Ye,T.Y.(2022).A novel two-party semiquantum keydistribution protocol based on GHZ-like states.Scientia Sinica Physica,Mechanica&Astronomica,52(12),120312.

[0022]

[17] Zhang,X.Z.,Gong,W.G.,Tan,Y.G.,Ren,Z.Z.,&Guo,X.T.(2009).Quantumkey distribution series network protocol with M-classical Bobs.ChinesePhysics B,18(6),2143.

[0023]

[18] Zhou,N.R.,Zhu,K.N.,&Zou,X.F.(2019).Multi-party semi-quantum keydistribution protocol with four-particle cluster states.Annalen der Physik,531(8),1800520.

[0024]

[19] Tian,Y.,Li,J.,Ye,C.Q.,&Li,C.Y.(2022).Multi-party semi-quantum keydistribution protocol based on hyperentangled Bell states.Frontiers inPhysics,10,1023443.

[0025]

[20] Pan,H.M.(2024).Multi-party semiquantum key distribution withmulti-qubit GHZ states.Quantum Information Processing,23,50.

[0026]

[21] Tsai,C.W.,&Wang,C.H.(2024).Multi-party quantum key distributionprotocol in quantum network.EPJ Quantum Technology,11,63.

[0027]

[22] Liu,D.,Chen,J.L.,&Jiang,W.(2012).High-capacity quantum securedirect communication with single photons in both polarization and spatial-mode degrees of freedom.International Journal of Theoretical Physics,51,2923-2929.

[0028]

[23] Yang,Y.G.,Xia,J.,Jia,X.,&Zhang,H.(2013).Comment on quantumprivate comparison protocols with a semi-honest third party.QuantumInformation Processing,12(2),877.

[0029]

[24] Cai,Q.Y.(2006).Eavesdropping on the two-way quantum communicationprotocols with invisible photons.Physics Letters A,351(1-2),23-25.

[0030]

[25] Gisin,N.,Ribordy,G.,Tittel,W.,&Zbinden,H.(2002).Quantumcryptography.Reviews of Modern Physics,74(1),145.

[0031]

[26] Deng,F.G.,Zhou,P.,Li,X.H.,Li,C.Y.,&Zhou,H.Y.(2005).Robustness oftwo-way quantum communication protocols against Trojan horse attack.https: / / arxiv.org / abs / quant-ph / 0508168.

[0032]

[27] Li,X.H.,Deng,F.G.,&Zhou,H.Y.(2006).Improving the security ofsecure direct communication based on the secret transmitting order ofparticles.Physical Review A,74(5),054302.

[0033]

[28] Gao,F.,Qin,S.J.,Wen,Q.Y.,&Zhu,F.C.(2007).A simple participantattack on the brádler- protocol.Quantum Information&Computation,7(4),329-334.

[0034]

[29] Zhang,C.,Huang,Q.,Long,Y.X.,&Sun,Z.W.(2021).Secure three-partysemi-quantum summation using single photons.International Journal ofTheoretical Physics,60,3478-3487.

[0035]

[30] Ye,T.Y.,Xu,T.J.,Geng,M.J.,&Chen,Y.(2022).Two-party securesemiquantum summation against the collective-dephasing noise.QuantumInformation Processing,21(3),118.

[0036]

[31] Hu,J.L.,&Ye,T.Y.(2022).Three-party secure semiquantum summationwithout entanglement among quantum user and classical users.InternationalJournal of Theoretical Physics,61(6),170.

[0037]

[32] Chou, W. H., Hwang, T., & Gu, J. (2016). Semi-quantum private comparison protocol under an almost-dishonest third party. https: / / arxiv.org / abs / 1607.07961.

[0038]

[33] Lang, Y. F. (2018). Semi-quantum private comparison using single photons. International Journal of Theoretical Physics, 57, 3048 - 3055.

[0039]

[34] Lin, P. H., Hwang, T., & Tsai, C. W. (2019). Efficient semi-quantum private comparison using single photons. Quantum Information Processing, 18, 207.

[0040]

[35] Xu, X., Lian, J. Y., & Ye, T. Y. (2024). Semiquantum private comparison via cavity QED. Quantum Information Processing, 23, 174.

[0041]

[36] Lian, J. Y., Li, X., & Ye, T. Y. (2023). Multi-party semiquantum private comparison of size relationship with d-dimensional Bell states. EPJ Quantum Technology, 10, 10.

[0042]

[37] Li, Q., Chan, W. H., & Long, D. Y. (2010). Semiquantum secret sharing using entangled states. Physical Review A, 82(2), 022303. Summary of the Invention

[0043] The purpose of the present invention is to provide a method for constructing a semi-quantum key distribution network based on single photons with polarization and empty mode degrees of freedom, so as to achieve the goal of "a participant with full quantum capabilities establishes different keys with each semi-quantum participant, and at the same time helps every two adjacent semi-quantum participants to establish different keys".

[0044] A method for constructing a semi-quantum key distribution network based on single photons with polarization and empty mode degrees of freedom includes the following six processes:

[0045] S1) Quantum participant TP randomly Base or Based on the above, 8nN double-degree-of-freedom single photons are prepared and divided into N sequences, namely Where Z P ={|H>,|V>},Z S ={|b1>,|b2>},X P ={|R>,|A>},X S ={|s>,|a>}, TP will S i The single photons are sent one by one to the semi-quantum participant P i Except for the first single photon, TP will send the next single photon only after receiving the previous single photon back.

[0046] S2) When receiving S i When a single photon is generated, the half-quantum participant P i After randomly performing CTRL or SITF operations on it, it is sent to the semi-quantum participant P. (i+1)modN Here, CTRL operation means no interference to single photons, and SITF operation means using The basis measures a single photon and prepares a new single photon in the same state. i P i The single photon sequences formed after SIFT operation and CTRL operation are respectively denoted as S i _SIFT sequence and S i _CTRL sequence. Here, i∈{0,1,…,N-1}.

[0047] S3) When receiving the message from P i When a single photon is emitted, P (i+1)modN Perform SIFT or unitary operations on it randomly (i.e. ) and then sent to TP. i _SIFT sequence is P (i+1)modN The sequences formed after SIFT operation and unitary operation are respectively denoted as S i _SIFT_SIFT sequence and Si _SIFT_U sequence, S i _CTRL sequence via P (i+1)modN The sequences formed after SIFT operation and unitary operation are respectively denoted as S i _CTRL_SIFT sequence and S i _CTRL_U sequence. Here, i∈{0,1,…,N-1}, k,l∈{0,1}.

[0048] S4) For TP-P i -P (i+1)modN -TP loop, TP from S i Random selection single photon and publish the corresponding position, and require P i and P (i+1)modN Publish the corresponding operation and measurement results, and finally select the correct measurement basis shown in Table 1 to measure the received single photons. i The CTRL operation is selected and P (i+1)modN When the unitary operation is selected, TP i The initial preparation state of the selected single photon, P (i+1)modN For S i The unitary operation applied by the corresponding single photon in the _CTRL sequence and the use of the prepared basis pairs from P (i+1)modN Received S i The error rate is calculated from the measurement results of the corresponding single photons in the _CTRL_U sequence; when P i SIFT operation is selected and P (i+1)modN When the unitary operation is selected, TP i The initial preparation state of the selected single photon, P i For S i The single photon selected Base measurement results, P (i+1)modN For S i The unitary operation applied to the corresponding single photon in the SIFT sequence and the (i+1)modN Received S i The corresponding single photon in the _SIFT_U sequence The error rate is calculated based on the measurement results; when P i The CTRL operation is selected and P (i+1)modN When SIFT operation is selected, TP i The initial preparation state of the selected single photon, P (i+1)modN For S i The corresponding single photon in the _CTRL sequence The base measurement results and the (i+1)modN Received S iThe corresponding single photon in the _CTRL_SIFT sequence The error rate is calculated based on the measurement results; when P i SIFT operation is selected and P (i+1)modN When SIFT operation is selected, TP i The initial preparation state of the selected single photon, P i For S i The single photon selected Base measurement results, P (i+1)modN For S i _The corresponding single photon in the SIFT sequence The base measurement results and the (i+1)modN Received S i _SIFT_The corresponding single photon in the SIFT sequence The error rate is calculated based on the measurement results. If any error rate is unreasonably large, TP will consider the quantum channel unsafe and terminate the communication early. i If the proportion of SIFT operations in the published operations is unreasonably high, the communication will be terminated prematurely. Here, i∈{0,1,…,N-1}.

[0049] Table 1 In TP-P i -P (i+1)modN Correct measurement basis for TP in the loop

[0050]

[0051] S5) For TP-P i -P (i+1)modN -TP loop, in order to detect whether TP is loyal, P i From S i Random selection The single photon is published and the corresponding position is announced, and then TP is required to announce the S i The initial preparation state of the selected single photon. If TP is Base preparation i Selected S i single photon, TP will randomly use Base or Base measurement from P (i+1)modN The corresponding single photon received; if TP is Base preparation i Selected S i single photon, TP will randomly use Base or Base measurement from P (i+1)modN The corresponding single photon received. i TP is required to publish the measurement results. There are six situations:

[0052] Situation ①: P i Select SIFT operation, P (i+1)modN Select any one of SIFT operation and unitary operation, while TP selects In this case, TP is measured based on Base preparation i Selected S i A single photon. i With P (i+1)modN According to my own operation and measurement results and the initial preparation state and Z published by TP P (Z S ) to calculate the error rate based on the measurement results;

[0053] Situation ②: P i Select SIFT operation, P (i+1)modN Select any one of SIFT operation and unitary operation, while TP selects In this case, TP can be measured with It is possible that Base preparation i Selected S i When TP is Base preparation i Selected S i When a single photon is emitted, P i With P (i+1)modN According to my own operation and measurement results and the initial preparation state and The error rate of the base measurement results calculation;

[0054] Situation ③:P i Select the CTRL operation, P (i+1)modN The unitary operation is selected, while TP selects In this case, TP is measured based on Base preparation i Selected S i A single photon. i With P (i+1)modN According to your own operation and the initial preparation state and The error rate of the base measurement results calculation;

[0055] Situation ④: P i Select the CTRL operation, P (i+1)modN The unitary operation is selected, while TP selects In this case, TP can be measured with It is possible that Base preparationi Selected S i When TP is Base preparation i Selected S i When a single photon is emitted, P i With P (i+1)modN According to my own operation and the initial preparation state and Z published by TP P (Z S ) to calculate the error rate based on the measurement results;

[0056] Situation ⑤:P i Select the CTRL operation, P (i+1)modN The SIFT operation was selected, while TP selected In this case, TP is measured based on Base preparation i Selected S i A single photon. i With P (i+1)modN According to my own operation and measurement results and the initial preparation state and Z published by TP P (Z S ) Calculate the error rate based on the measurement results;

[0057] Situation 6: P i Select the CTRL operation, P (i+1)modN The SIFT operation was selected, while TP selected In this case, TP can be measured with It is possible that Base preparation i Selected S i When TP is Base preparation i Selected S i When a single photon is emitted, P i With P (i+1)modN According to your own operation and the initial preparation state and The error rate is calculated based on the measurement results.

[0058] If the error rate of any of the above six situations is unreasonably large, P i and P (i+1)modN The TP will be considered as disloyal and the communication will be terminated prematurely. Here, i∈{0,1,…,N-1}.

[0059] S6) For TP-P i -P (i+1)modN -S in TP loop i The remaining 4n single photons, P i and P (i+1)modNPublish the type of operation applied separately.

[0060] TP to P (i+1)modN Received S i The corresponding remaining single photons in the _SIFT_U sequence are Base measurement, and publish their own S i The initial preparation basis of the corresponding single photon in Base preparation S i When the corresponding single photon in S (Z P )Based on the measurement results. TP to S i The initial prepared state of the corresponding single photon is represented as |φ>, and the polarization state and empty mode of |φ> are represented as |S i _P> and |S i _S>,P i Yes | i _P> and |S i The measurement results of |S i _SIFT_P> and |S i _SIFT_S>,P (i+1)modN Yes | i _SIFT_P> and |S i The unitary operations applied by _SIFT_S> are denoted as S i _U P and S i _U S ,TP to P (i+1)modN Received S i _U P |S i _SIFT_P> and S i _U S |S i The measurement results of _SIFT_S> are represented as |S i _TP_P> and |S i _TP_S>. If the initial preparation base of TP is The following relationship will exist: If the initial preparation base of TP is The following relationship will exist: In this way, P i and P (i+1)modN Can be easily shared by E(|S i _SITF_S>) and E(|S i _SITF_P>) i((i+1)modN) , where K i((i+1)modN) The length of is n bits, that is here,

[0061] TP selects the correct measurement basis pair from P (i+1)modN Received S i _CTRL_U sequence and publish their own S i The initial preparation basis of the corresponding single photon in TP i The initial preparation state of the corresponding single photon in is expressed as The polarization state and empty mode of are represented as |S i _P'> and |S i _S'>,P (i+1)modN Yes | i _P'> and |S i The unitary operations applied by _S'> are denoted as S i _U' P and S i _U' S ,TP to P (i+1)modN Received S i _U' P |S i _P'> and S i _U' S |S i The measurement results of |S i _TP_P'> and |S i _TP_S'>. If the initial preparation base of TP is The following relationship will exist: If the initial preparation base of TP is The following relationship will exist: Therefore, P (i+1)modN and TP can be easily shared by E(S i _U' P ) and E(S i _U' S ) composed of a key K T((i+1)modN) , where K T((i+1)modN) The length of is n bits, that is Here, i∈{0,1,…,N-1}. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The network structure of the method of the present invention is given when N=3; Figure 2 For Eve through and The entanglement-measurement attack launched; Figure 3 (a) and 3(b) respectively prepare and measure the quantum circuit of |Vs> and its simulation results; Figure 4(a) and 4(b) are the quantum circuits where P0, P1, and P2 all select the CTRL operation and P1, P2, and P0 all select the unitary operation, and their simulation results; Figure 5 (a) and 5(b) are the quantum circuits where P0, P1, and P2 all select the SIFT operation and P1, P2, and P0 all select the unitary operation, and their simulation results; Figure 6 (a) and 6(b) are the quantum circuits of the measurement - resend attack initiated by Eve and their simulation results. Detailed implementation manners

[0063] The technical solution of the present invention will be further described below in conjunction with embodiments.

[0064] 1 Method description

[0065] A single - photon |φ> with polarization and spatial - mode dual degrees of freedom can be defined as:

[22]

[0066]

[0067] where |φ> P ∈{|H>, |V>, |S>, |A>} and |φ> S ∈{|b1>, |b2>, |s>, |a>} are the polarization state and spatial mode of |φ>, respectively. Here, there are

[0068]

[0069] where |H> and |V> are the horizontal polarization and vertical polarization of the photon, respectively, and |b1> and |b2> are the upper spatial mode and lower spatial mode of the photon, respectively. Two non - orthogonal measurement bases of a single - photon in the polarization degree of freedom can be defined as Z P ={|H>, |V>} and X P ={|R>, |A>}, and two non - orthogonal measurement bases of a single - photon in the spatial - mode degree of freedom can be defined as Z S ={|b1>, |b2>} and X S ={|s>, |a>}.

[0070] Two unitary operations of a single - photon in the polarization degree of freedom can be described as I P =|H><H| + |V><V| and U P =|V><H| + |H><V|, and two unitary operations of a single - photon in the spatial - mode degree of freedom can be described as I S =|b1><b1 + |b2><b2| and U S =|b2><b1| + |b1><b2|. It is easy to obtain:

[0071]

[0072] Obviously, U P and U S Neither will change the measurement basis of the corresponding degrees of freedom.

[0073] definition Where k,l∈{0,1}, then

[0074]

[0075] Here, the definition

[0076]

[0077] Assume that there are N half-quantum participants P0, P1, ..., P N-1 and a quantum participant TP, where TP is semi-loyal, i.e., she is not allowed to collude with others but can impose any attack.

[23] P0,P1,…,P N-1 and TP intend to build an N+1 party semi-quantum key distribution network with the following functions: TP can communicate with P i Establishing a key and helping P i and P (i+1)modN Establish a key, where i∈{0,1,…,N-1}. Define an encoding function E(x) as shown in formula (6):

[0078]

[0079] The N+1-party half-quantum key distribution network construction method consists of the following steps:

[0080] S1)TP randomly Base or Based on the above, 8nN double-degree-of-freedom single photons are prepared and divided into N sequences, namely Where i∈{0,1,…,N-1}. TP converts S i The single photons are sent one by one to P i Except for the first single photon, TP will send the next single photon only after receiving the previous single photon back.

[0081] S2) When receiving S i When a single photon is emitted, P i Perform CTRL or SITF operations on it randomly and send it to P (i+1)modN Here, CTRL operation means no interference to single photons, and SITF operation means using The basis measures a single photon and prepares a new single photon in the same state. i P iThe single photon sequences formed after SIFT operation and CTRL operation are respectively denoted as S i _SIFT sequence and S i _CTRL sequence. Here, i∈{0,1,…,N-1}.

[0082] S3) When receiving the message from P i When a single photon is emitted, P (i+1)modN Perform SIFT or unitary operations on it randomly (i.e. ) and then sent to TP. i _SIFT sequence is P (i+1)modN The sequences formed after SIFT operation and unitary operation are respectively denoted as S i _SIFT_SIFT sequence and S i _SIFT_U sequence, S i _CTRL sequence via P (i+1)modN The sequences formed after SIFT operation and unitary operation are respectively denoted as S i _CTRL_SIFT sequence and S i _CTRL_U sequence. Here, i∈{0,1,…,N-1}, k,l∈{0,1}.

[0083] S4) For TP-P i -P (i+1)modN -TP loop, TP from S i Random selection single photon and publish the corresponding position, and require P i and P (i+1)modN Publish the corresponding operation and measurement results, and finally select the correct measurement basis shown in Table 1 to measure the received single photons. i The CTRL operation is selected and P (i+1)modN When the unitary operation is selected, TP i The initial preparation state of the selected single photon, P (i+1)modN For S i The unitary operation applied by the corresponding single photon in the _CTRL sequence and the use of the prepared basis pairs from P (i+1)modN Received S i The error rate is calculated from the measurement results of the corresponding single photons in the _CTRL_U sequence; when P i SIFT operation is selected and P (i+1)modN When the unitary operation is selected, TP i The initial preparation state of the selected single photon, P i For S i The single photon selected Base measurement results, P (i+1)modN For S iThe unitary operation applied to the corresponding single photon in the SIFT sequence and the (i+1)modN Received S i The corresponding single photon in the _SIFT_U sequence The error rate is calculated based on the measurement results; when P i The CTRL operation is selected and P (i+1)modN When SIFT operation is selected, TP i The initial preparation state of the selected single photon, P (i+1)modN For S i The corresponding single photon in the _CTRL sequence The base measurement results and the (i+1)modN Received S i The corresponding single photon in the _CTRL_SIFT sequence The error rate is calculated based on the measurement results; when P i SIFT operation is selected and P (i+1)modN When SIFT operation is selected, TP i The initial preparation state of the selected single photon, P i For S i The single photon selected Base measurement results, P (i+1)modN For S i _The corresponding single photon in the SIFT sequence The base measurement results and the (i+1)modN Received S i _SIFT_The corresponding single photon in the SIFT sequence The error rate is calculated based on the measurement results. If any error rate is unreasonably large, TP will consider the quantum channel unsafe and terminate the communication early. i If the proportion of SIFT operations in the published operations is unreasonably high, the communication will be terminated prematurely. Here, i∈{0,1,…,N-1}.

[0084] S5) For TP-P i -P (i+1)modN -TP loop, in order to detect whether TP is loyal, P i From S i Random selection The single photon is published and the corresponding position is announced, and then TP is required to announce the S i The initial preparation state of the selected single photon. If TP is Base preparation i Selected S i single photon, TP will randomly use Base or Base measurement from P (i+1)modNThe corresponding single photon received; if TP is Base preparation i Selected S i single photon, TP will randomly use Base or Base measurement from P (i+1)modN The corresponding single photon received. i TP is required to publish the measurement results. There are six situations:

[0085] Situation ①: P i Select SIFT operation, P (i+1)modN Select any one of SIFT operation and unitary operation, while TP selects In this case, TP is measured based on Base preparation i Selected S i A single photon. i With P (i+1)modN According to my own operation and measurement results and the initial preparation state and Z published by TP P (Z S ) to calculate the error rate based on the measurement results;

[0086] Situation ②: P i Select SIFT operation, P (i+1)modN Select any one of SIFT operation and unitary operation, while TP selects In this case, TP can be measured with It is possible that Base preparation i Selected S i When TP is Base preparation i Selected S i When a single photon is emitted, P i With P (i+1)modN According to my own operation and measurement results and the initial preparation state and The error rate of the base measurement results calculation;

[0087] Situation ③:P i Select the CTRL operation, P (i+1)modN The unitary operation is selected, while TP selects In this case, TP is measured based on Base preparation i Selected S i A single photon. i With P (i+1)modN According to your own operation and the initial preparation state and The error rate of the base measurement results calculation;

[0088] Situation ④: P i Select the CTRL operation, P (i+1)modN The unitary operation is selected, while TP selects In this case, TP can be measured with It is possible that Base preparation i Selected S i When TP is Base preparation i Selected S i When a single photon is emitted, P i With P (i+1)modN According to my own operation and the initial preparation state and Z published by TP P (Z S ) to calculate the error rate based on the measurement results;

[0089] Situation ⑤:P i Select the CTRL operation, P (i+1)modN The SIFT operation was selected, while TP selected In this case, TP is measured based on Base preparation i Selected S i A single photon. i With P (i+1)modN According to my own operation and measurement results and the initial preparation state and Z published by TP P (Z S ) Calculate the error rate based on the measurement results;

[0090] Situation 6: P i Select the CTRL operation, P (i+1)modN The SIFT operation was selected, while TP selected In this case, TP can be measured with It is possible that Base preparation i Selected S i When TP is Base preparation i Selected S i When a single photon is emitted, P i With P (i+1)modN According to your own operation and the initial preparation state and The error rate is calculated based on the measurement results.

[0091] If the error rate of any of the above six situations is unreasonably large, P i and P (i+1)modNThe TP will be considered as disloyal and the communication will be terminated prematurely. Here, i∈{0,1,…,N-1}.

[0092] S6) For TP-P i -P (i+1)modN -S in TP loop i The remaining 4n single photons, P i and P (i+1)modN Publish the type of operation applied separately.

[0093] TP to P (i+1)modN Received S i The corresponding remaining single photons in the _SIFT_U sequence are Base measurement, and publish their own S i The initial preparation basis of the corresponding single photon in Base preparation S i When the corresponding single photon in S (Z P )Based on the measurement results. TP to S i The initial prepared state of the corresponding single photon is represented as |φ>, and the polarization state and empty mode of |φ> are represented as |S i _P> and |S i _S>,P i Yes | i _P> and |S i The measurement results of |S i _SIFT_P> and |S i _SIFT_S>,P (i+1)modN Yes | i _SIFT_P> and |S i The unitary operations applied by _SIFT_S> are denoted as S i _U P and S _ _U S ,TP to P (i+1)modN Received S i _U P |S i _SIFT_P> and S i _U S |S i The measurement results of _SIFT_S> are represented as |S i _TP_P> and |S i _TP_S>. If the initial preparation base of TP is The following relationship will exist:

[0094]

[0095] If the initial preparation base of TP is The following relationship will exist:

[0096]

[0097] According to formula (8) and formula (9), P i and P (i+1)modN Can be easily shared by E(|S i _SITF_S>) and E(|S i _SITF_P>) i((i+1)modN) , where K i((i+1)modN) The length of is n bits, that is Here, i∈{0,1,…,N-1}.

[0098] TP selects the correct measurement basis pair from P (i+1)modN Received S i _CTRL_U sequence and publish their own S i The initial preparation basis of the corresponding single photon in TP i The initial preparation state of the corresponding single photon in is expressed as The polarization state and empty mode of are represented as |S i _P'> and |S i _S'>,P (i+1)modN Yes | i _P'> and |S i The unitary operations applied by _S'> are denoted as S i _U' P and S i _U' S ,TP to P (i+1)modN Received S i _U' P |S i _P'> and S i _U' S |S i The measurement results of |S i _TP_P'> and |S i _TP_S'>. If the initial preparation base of TP is The following relationship will exist:

[0099]

[0100] If the initial preparation base of TP is The following relationship will exist:

[0101]

[0102] Therefore, P(i+1)modN and TP can be easily shared by E(S i _U' P ) and E(S i _U' S ) T((i+1)modN) , where K T((i+1)modN) The length of is n bits, that is Here, i∈{0,1,…,N-1}.

[0103] 2 Safety Analysis

[0104] 2.1 External Attacks

[0105] (1) Intercept-Retransmit Attack

[0106] Eve intercepts TP and sends it to P i S i The single photon prepared randomly in Base or The pseudo single photon of the basis is sent to P i Apparently, Eve only has Eve’s attack will inevitably be discovered in step S4, because no matter the initial prepared state of TP or P i and P (i+1)modN The operation is random to Eve. For a single photon selected for eavesdropping detection in step S4, when P i Select CTRL and P (i+1)modN For P i When performing unitary operations on single photons, Eve will The probability of being detected; when P i Select CTRL and P (i+1)modN For P i When performing SIFT operations on single photons, Eve will The probability of being detected; when P i Select SIFT operation and P (i+1)modN For P i When performing unitary operations on single photons, Eve will The probability of being detected; when P i Select SIFT operation and P (i+1)modN For P i When performing SIFT operations on single photons, Eve will The probability that a single photon is selected for eavesdropping detection in step S4 is Therefore, Eve is very interested in S iThe probability that the intercept-retransmission attack launched will be detected is

[0107]

[0108] When n is large enough, Eve will be detected in step S4 with a probability approaching 1. Here, i∈{0,1,…,N-1}.

[0109] (2) Measurement-Retransmission Attack

[0110] Eve intercepts TP and sends it to P i single photon, using The basis measures it and regenerates a new single photon in the same state, which is then sent to P i Eve's attack will inevitably be discovered in step S4, because Eve's measurement will destroy the original state of the single photon. For a single photon selected for eavesdropping detection in step S4, when P i When SIFT operation is selected, regardless of P (i+1)modN For P i Whether the single photon is subjected to SIFT operation or unitary operation, Eve will be detected with a probability of 0; i Select CTRL and P (i+1)modN For P i When SIFT operation is performed on single photons, Eve will be detected with a probability of 0; when P i Select CTRL and P (i+1)modN For P i When performing unitary operations on single photons, Eve will The probability that a single photon is selected for eavesdropping detection in step S4 is Therefore, Eve is very interested in S i The probability that the launched measurement-retransmission attack will be detected is

[0111]

[0112] When n is large enough, Eve will be found in step S4 with a probability approaching 1. Here, i∈{0,1,…,N-1}.

[0113] (3) Entanglement-Measurement Attack

[0114] Eve's entanglement-measurement attack is available Figure 2 To express. [9,10] Specifically, Eve sends TP to P i The single photon and P i Send to P (i+1)modN The single photons are respectively executed and in and are two unitary operations in the common exploration space of Eve with a shared initial state of |ε>. Here, i∈{0,1,…,N-1}.

[0115] Theorem 1: Assume that Eve launches an entanglement-measurement attack such as Figure 2 In order to avoid any error in step S4, the final state of Eve’s detection state should be consistent with P i and P (i+1)modN The operation and measurement results are irrelevant, so Eve cannot get any information about K i((i+1)modN) and K T((i+1)modN) Any useful information.

[0116] Proof: The initial state prepared by TP The global state of the composite system composed of |φ>|ε> and Eve's |ε> can be expressed as |φ>|ε>, where |φ> is determined by TP randomly changing Base or Base generation. Execute in Eve After that, the global state changes to

[0117]

[0118] in and is the unnormalized state of Eve's probe particle. Without loss of generality, we assume that the initial preparation state of TP is |Hs>.

[0119] After receiving a single photon from TP, P i After randomly applying CTRL operation or SIFT operation, it is randomly sent to P (i+1)modN When receiving a i When a single photon is emitted, P (i+1)modN Perform SIFT or unitary operations on it randomly (i.e. ) and then sent to TP. Two cases are discussed separately here.

[0120] ①P i When SITF operation is applied, the global state of equation (15) will be randomly collapsed to and Eve in P i Send to P (i+1)modN The single photon is applied Regardless of P (i+1)modN For P iWhether the single photon is SIFT or unitary, in order to prevent Eve's attack from causing any errors in step S4, both must satisfy

[0121]

[0122] That is to say, Cannot change P i The state of a single photon obtained by collapse after applying SITF operation.

[0123] ②P i The situation of applying CTRL operation. Eve is in P i Send to P (i+1)modN The single photon is applied According to equations (16-19), the global state of equation (15) will be transformed into

[0124]

[0125] When P (i+1)modN For P i In order to prevent Eve's attack from causing any errors in step S4, it is necessary to satisfy

[0126]

[0127] When P (i+1)modN For P i When a single photon is subjected to SIFT operation, the global state of equation (20) will be randomly collapsed to and According to equations (21) and (22), Eve's attack does not cause any error in step S4.

[0128] ③ In summary, when the initial preparation state of TP is |Hs>, in order to prevent Eve’s attack from causing any errors in step S4, the final state of Eve’s detection state should be the same as P i and P (i+1)modN The operation and measurement results are irrelevant, so Eve cannot get any information about K i((i+1)modN) and K T((i+1)modN) Any useful information.

[0129] It is not difficult to find that when the initial preparation state of TP is Base or When the other quantum states of the basis are taken into account, the similar method can be used to prove that Theorem 1 is true.

[0130] (4) Trojan Horse Attack

[0131] Eve can use the photons transmitted back and forth to launch a Trojan horse attack to try to obtain useful information. Eve can launch an invisible photon eavesdropping attack

[24] and delayed photon Trojan attack [25,26] According to the literature [26,27], quantum signal receivers can use wavelength filters and photon number dividers in front of their own devices to defend against invisible photon eavesdropping attacks and delayed photon Trojan horse attacks, respectively.

[0132] 2.2 Internal Attack

[0133] In 2007, Gao et al.

[28] For the first time, a new attack called participant attack is proposed. Since participants participate in the execution of communication, their threat is often greater than that of external eavesdropper Eve. The following is a detailed analysis of participant attack.

[0134] (1) Attacks from Disloyal Semi-Quantum Participants

[0135] For TP-P i -P (i+1)modN -TP loop,P i Might try to get K T((i+1)modN) . Due to K T((i+1)modN) is the S in step S6 i The corresponding remaining single photons of the _CTRL_U sequence are generated, P i No information about K can be obtained when not attacking T((i+1)modN) If P i For S i The 8n single photons are all subjected to SIFT operation, and there will be no K T((i+1)modN) , but P i The proportion of SIFT operations published in step S4 will be unreasonably high, P i will be considered disloyal and the communication will be terminated prematurely. i The following attacks may be launched: i For S i After applying the CTRL operation to the single photon, it is saved in one's own hand, and a random The pseudo single photon of the basis is sent to P (i+1)modN ;use Base measurement P (i+1)modN After the operation, the pseudo single photon is decoded into P (i+1)modN The operation is applied and applied to S which is kept in its own hands i The single photon is then sent to TP. (i+1)modN When you select CTRL, P i This attack will not be detected by TP in step S4. (i+1)modNWhen SIFT operation is selected, P i This attack will be detected by TP as an external attack in step S4 because when P (i+1)modN When choosing to perform SIFT operation, TP is used for S i The initial preparation state of the single photon, P (i+1)modN For false photons The basic measurement results and TP for the received single photon The three base measurement results may not necessarily correspond to each other completely correctly. Here, i∈{0,1,…,N-1}.

[0136] For TP-P i -P (i+1)modN -TP loop,P t Might try to get K i((i+1)modN) and K T((i+1)modN) , where t,i∈{0,1,…,N-1} and t≠i,(i+1)modN. At this time, P t For TP-P i -P (i+1)modN -TP loop does not play the role of a participant, so P t Any attack launched will be detected by TP in step S4.

[0137] For TP-P i -P (i+1)modN -TP loop, except P i and P (i+1)modN Two or more semi-quantum participants may also join together to try to obtain K i((i+1)modN) and K T((i+1)modN) , but they will also be detected by TP as external eavesdroppers in step S4. Here, i∈{0,1,…,N-1}.

[0138] (2) Attacks from Semi-loyal TPs

[0139] TP, as a semi-loyal third party, may try to obtain K i((i+1)modN) TP Base preparation S i All single photons, but in step S5 they are still published as the preparation basis or TP's attack strategy can easily pass the eavesdropping detection in step S4, because the eavesdropping detection in step S4 is dominated by TP. However, TP's attack strategy cannot pass the eavesdropping detection in step S5, because TP is controlled by P. i and P (i+1)modN Requires that the initial preparation state and measurement results be published before P i and P (i+1)modNI don't know anything about the operation.

[0140] Example:

[0141] 1. Simulation of the method of the present invention

[0142] Here, the IBM quantum computing cloud platform Qiskit is used to simulate the method of the present invention when N=3 to prove its correctness. Each simulation experiment is performed 10,000 times. For the convenience of description, the simulation process ignores the eavesdropping detection process as much as possible.

[0143] 1.1 Preparation and measurement of quantum states

[0144] In step S1 of the method of the present invention, TP is randomly and Without loss of generality, assuming that TP prepares |Vs>, the quantum circuit for preparing and measuring |Vs> is as follows Figure 3 (a) is shown. Figure 3 In (a), the left side of the first dotted line represents the preparation of the quantum state, where q1 and q0 represent two qubits whose initial quantum states are both |0>. |Vs> can be generated by performing a NOT gate (i.e., X gate) on q1 and a Hadamard gate (i.e., H gate) on q0. |Vs> can be prepared in the same way for q3 and q2. The right side of the first dotted line represents the measurement of the quantum state. Base measurement, performed on lines q3 and q2 Base measurement. Figure 3 The simulation results of (a) are as follows Figure 3 (b) is shown. Figure 3 In (b), the last two digits of the register result 10 indicates The base measurement result is always |Vs>; the first two digits of the register are 10 and 11, and the ratio is close to 1:1, which satisfies The theoretical results of the base measurement show that |Vs> After the basis is measured, it is randomly collapsed into |Vb1> and |Vb2>.

[0145] 1.2 Simulation of the method of the present invention

[0146] In the method of the present invention, TP is randomly or The initial single photon is then sent to P i ;P i The initial single photon received from TP is randomly subjected to CTRL or SIFT operation and then sent to P. (i+1)mod3 ;P (i+1)mod3 In the pair from P iThe received single photons are sent to TP after SIFT operation or unitary operation. i((i+1)mod3) and K T((i+1)mod3) Here, i∈{0,1,2}.

[0147] First, we discuss the case where P0, P1, and P2 all choose CTRL operation and P1, P2, and P0 all choose unitary operation. The corresponding quantum circuit and simulation results are shown in Figure 4 As shown. Figure 4 In (a), the left side of the first dotted line represents: TP randomly prepares quantum states |Hs>, |Ab2> and |Vs> (corresponding to q5q4, q3q2 and q1q0 respectively) and sends them to P0, P1 and P2 respectively, then P0, P1 and P2 perform CTRL operation on the single photon received from TP and send it to P1, P2 and P0 respectively; the left side of the second dotted line represents that P1, P2 and P0 perform CTRL operation on the single photon received Then send it to TP; the second dotted line and the right side of the third dotted line represent TP using base, Motowa The basis measures the single photons received from P1, P2 and P0 respectively. Figure 4 In (b), from left to right, the 1st to 6th bits in the simulation result are the measurement results of TP. Here r(j) represents the value of the jth bit of the simulation result, where j∈{1,2,…,6}. It is not difficult to find that the following relationship exists:

[0148]

[0149] where |H>, |b2>, |V> are some of the initial prepared states of TP, U P ,I S , U P are the unitary operations performed by P1, P2, and P0 on |H>, |b2>, and |V>, respectively. TP will publish the preparation basis of the initial state. P1, P2, and P0 can be calculated by K T1 =E(U P )=1、K T2 =E(I S )=0 and K T0 =E(U P )=1 to generate the key. TP is calculated by and To establish keys with P1, P2 and P0 respectively. Therefore, the simulation results of the quantum circuit in this case are consistent with the method of the present invention.

[0150] Next, we discuss the case where P0, P1, and P2 all perform SIFT operations and P1, P2, and P0 all choose unitary operations. The corresponding quantum circuits and simulation results are shown in Figure 5 As shown. Figure 5 In (a), the left side of the first dotted line represents that TP randomly prepares quantum states |Hs>, |Ab2> and |Vs> (corresponding to q5q4, q3q2 and q1q0 respectively) and sends them to P0, P1 and P2 respectively; the left side of the second dotted line represents that P0, P1 and P2 perform SIFT operations on the single photons received from TP. The third dotted line on the left represents that P0, P1 and P2 regenerate new single photons in the same quantum state according to the measurement results stored in registers a, b and c (corresponding to q 11 q 10 , q9q8 and q7q6) and send them to P1, P2 and P0 respectively; the left side of the fourth dotted line represents that P1, P2 and P0 all execute The fourth dotted line on the right represents TP’s processing of the single photons received from P1, P2, and P0. The base measurement is performed and the measurement results are stored in register tp. Figure 5 In (b), from left to right, the 1st to 6th bits in each simulation result are the measurement results of TP, and the 7th to 12th bits are the measurement results of P0, P1 and P2 performing SIFT operations. Here r(j) represents the value of the jth bit of the simulation result, where j∈{1,2,…,12}. It is not difficult to find that the following relationship exists:

[0151]

[0152] Here 101010 corresponds to the execution of P1, P2 and P0 respectively. TP will publish the values ​​of r(2), r(3) and r(6), and P1 can calculate Establish key K with P0 01 = r(8), P2 can be calculated by Establish key K with P1 12 = r(9), P0 can be calculated by Establish a key K with P2 02 = r(12). Therefore, the simulation results of the quantum circuit in this case are consistent with the method of the present invention.

[0153] 1.3 Simulation of the measurement-retransmission attack launched by Eve

[0154] Here, we take the case where P0, P1, and P2 all choose the CTRL operation and P1, P2, and P0 all choose the unitary operation as an example to analyze the measurement-retransmission attack initiated by Eve. The corresponding quantum circuit is as follows Figure 6 (a). Figure 6 (a), Eve The base measures the quantum state sent out when P0, P1 and P2 select the CTRL operation and stores the measurement result in register eve, then regenerates a new single photon in the same state and sends it to P1, P2 and P0 respectively; P1, P2 and P0 perform the received single photon Then send it to TP; finally, TP performs quantum measurement on the received single photon with the prepared basis. If Eve does not exist, the simulation result should be as follows Figure 6 (b) shows that the measurement results of TP should be 101100. However, Figure 6 Among the 64 measurement results of (b), only 8 are 101100, so Eve's measurement-retransmission attack will undoubtedly be detected.

[0155] 2 Discussions

[0156] Quantum bit efficiency is an important indicator for evaluating the performance of quantum communication methods and is defined as: [4]

[0157]

[0158] where ρ k is the number of bits of the generated classical key, ρ q is the number of qubits consumed, ρ c is the number of classical bits consumed by the classical communication process. The classical bits used for eavesdropping detection are ignored here.

[0159] In the method of the present invention, K i((i+1)modN) The length of K is n bits. T((i+1)modN) The length of is also n bits, where i∈{0,1,…,N-1}, so ρ k =nN+nN=2nN. TP is randomly assigned in step S1 Base or Generate 8nN double-degree-of-freedom single photons and divide them into N sequence, that is where i∈{0,1,…,N-1}; TP converts S i The single photons are sent one by one to P i ; When receiving S i When a single photon is emitted, P i Perform CTRL or SITF operations on it randomly and send it to P (i+1)modN ; When receiving from Pi When a single photon is emitted, P (i+1)modN Perform SIFT or unitary operations on it randomly (i.e. ) and then sent to TP; therefore, ρ q =8nN×2+4nN×2+4nN×2=32nN. In step S6, for TP-P i -P (i+1)modN -S in TP loop i The remaining 4n single photons, P i and P (i+1)modN Publish the type of operation applied separately; TP (i+1)modN Received S i The corresponding remaining single photons in the _SIFT_U sequence are Base measurement, and publish their own S i The initial preparation basis of the corresponding single photon in Base preparation S i When the corresponding single photon in S (Z P ) basis measurement results; TP selects the correct measurement basis pair from P (i+1)modN Received S i _CTRL_U sequence and publish their own S i The initial preparation basis of the corresponding single photon in c =4nN×2+nN+nN+nN=11nN. It is not difficult to conclude that the quantum bit efficiency of the method of the present invention is

[0160] Next, the method of the present invention is compared in detail with the MSQKD method in references [17-21], and the comparison results are summarized in Table 2. The method of the present invention uses a single photon with two degrees of freedom, avoiding the use of quantum entangled states, so the method of the present invention is superior to the methods in references [18-21] in terms of quantum resources; the method of the present invention only requires quantum participants to perform single photon measurements, avoiding quantum entangled state measurements, so the method of the present invention is superior to the methods in references [18-20] in terms of quantum participant measurements; the method of the present invention does not require half-quantum participants to perform Hadamard operations, so the method of the present invention is superior to the method in reference

[21] in terms of half-quantum participants performing Hadamard operations; in terms of functions, only the method of the present invention can realize the function of "a quantum participant establishes different keys with each half-quantum participant, and at the same time helps every two adjacent half-quantum participants to establish different keys".

[0161] Table 2 Comparison of different MSQKD methods

[0162]

[0163] 3. Application of the method of the present invention

[0164] 3.1 Application to half-quantum summation

[0165] The purpose of half-quantum summation [29-31] is to calculate the sum of the secret data of the half-quantum participants without revealing the secret data of the half-quantum participants. Next, the method of the present invention is applied to the half-quantum summation.

[0166] Semi-quantum participant P i The binary secret sequence is M i , where i∈{0,1,…,N-1}. P0,P1,…,P N-1 Want to calculate M0, M1, ..., M with the help of a semi-loyal quantum third party TP N-1 The modulo 2 sum of M0,M1,…,M N-1 Disclosure to others besides the holder. This can be achieved using the following methods.

[0167] Steps 1-6 are the same as steps S1-S6 of the method of the present invention.

[0168] Step 7: P i calculate

[0169]

[0170] And through the certified classical channel, R i Sent to TP, where i∈{0,1,…,N-1}. TP calculation

[0171]

[0172] And to P0,P1,…,P N-1 Announced by R.

[0173] 3.2 Application to Semi-Quantum Privacy Comparison

[0174] Semi-quantum privacy comparison [32-36] aims to compare the equality or size relationship of secret data without revealing the secret data of semi-quantum participants. Next, the method of the present invention is applied to semi-quantum privacy comparison.

[0175] (1) Application to semi-quantum privacy equality comparison

[0176] Semi-quantum participant P i The binary secret sequence is M i , where i∈{0,1,…,N-1}. i and P (i+1)modN Want to determine M with the help of a semi-loyal quantum third party TP i and M(i+1)modN Are they equal, but M cannot be i and M (i+1)modN Disclosure to others besides the holder. This can be achieved using the following methods.

[0177] Steps 1-6 are the same as steps S1-S6 in Part 2.

[0178] Step 7: P i calculate

[0179]

[0180] P (i+1)modN calculate

[0181]

[0182] Then, P i and P (i+1)modN R i and R (i+1)modN Sent to TP via authenticated classical channel. TP calculation

[0183]

[0184] And to P i and P (i+1)modN Publish R. If R is a sequence of all zeros, P i and P (i+1)modN It will be considered that M i and M (i+1)modN equal; otherwise, P i and P (i+1)modN It will be considered that M i and M (i+1)modN Not equal.

[0185] (2) Application to semi-quantum privacy size comparison

[0186] Semi-quantum participant P i The secret integer is M i , where M i ∈{0,1,…,h},i∈{0,1,…,N-1} and P i and P j Want to determine M with the help of a semi-loyal quantum third party TP i and M j The size relationship, but M i and M j Leak to others other than the holder, where i,j∈{0,1,…,N-1} and i≠j. The following method can be used to achieve this goal. Here, and They represent sum modulo d and minus modulo d respectively.

[0187] Steps 1-6 are the same as steps S1-S6 in Part 2.

[0188] Step 7: K Ti , K T((i+1)modN) and K i((i+1)modN) Every Each bit is converted into a d-ary number to form a new key sequence K' Ti , K' T((i+1)modN) and K i ' ((i+1)modN) ,in P stands for round up. i calculate

[0189]

[0190] P (i+1)modN calculate

[0191]

[0192] Then, P i and P (i+1)modN R i and R (i+1)modN Sent to TP via authenticated classical channel. TP calculation

[0193]

[0194] When i<j, TP calculation

[0195]

[0196] When i>j, TP calculation

[0197]

[0198] Here, i, j∈{0,1,…,N-1} and i≠j.

[0199] According to formula (34) and formula (35), if R ij = 0, then M i =M j ; If 0<R ij ≤h, then M i >M j ; If h<R ij ≤2h, then M i <M j Here, i, j∈{0,1,…,N-1} and i≠j. Finally, TP moves to P i and P j Announcement Mi and M j The size relationship.

[0200] 3.3 Application to Semi-Quantum Secret Sharing

[0201] Semi-quantum secret sharing

[37] aims to achieve one of the functions of "the secret data of a quantum participant is shared by multiple semi-quantum participants and the secret data of the quantum participant can only be recovered when these semi-quantum participants work together". Next, the method of the present invention is applied to semi-quantum secret sharing.

[0202] The binary secret sequence of quantum TP is M TP TP plans to make semi-quantum P0, P1, ..., P N-1 ShareM TP The following methods can be used to achieve this goal.

[0203] Steps 1-6 are the same as steps S1-S6 in Part 2.

[0204] Step 7: TP calculation

[0205]

[0206] And to P0,P1,…,P N-1 Publish R. Obviously, only when P0, P1, ..., P N-1 You can only get M when you work together TP .

[0207] 4 Conclusion

[0208] The present invention adopts single photons with polarization and empty mode degrees of freedom as quantum resources to propose a novel method for constructing a semi-quantum key distribution network, realizing the function of "a quantum participant establishes different keys with each semi-quantum participant, and at the same time helps each two adjacent semi-quantum participants to establish different keys". The method of the present invention does not require quantum entangled states, pre-shared keys, quantum entanglement exchange operations, quantum delay lines, and Hadamard operations, and only requires single photon measurement. The method of the present invention has been proven to be able to effectively prevent external and internal attacks. The simulation conducted by the IBM quantum computing cloud platform verifies the correctness of the method of the present invention. The method of the present invention can be applied to semi-quantum summation, semi-quantum privacy comparison, and semi-quantum secret sharing. Because the current technical conditions can easily realize the preparation, measurement, and application of unitary operations to single photons with polarization and empty mode degrees of freedom, the method of the present invention has good practical feasibility.

Claims

1. A method for constructing a semi-quantum key distribution network based on single photons with polarization and empty mode freedom, achieving the goal of "a participant with full quantum capabilities establishes different keys with each semi-quantum participant, and at the same time helps every two adjacent semi-quantum participants to establish different keys"; only single photons rather than quantum entangled states are needed as quantum resources and only single photon measurements are needed; no pre-shared keys, quantum entanglement exchange operations, quantum delay lines, and Hadamard operations are required; It includes the following six processes: S1) Quantum participant TP randomly Base or Base preparation 8n N Double-degree-of-freedom single photons are divided into N sequences, namely Where Z P ={|H>,|V>},Z S ={|b1>,|b2>},X P ={|R>,|A>},X S ={|s>,|a>}, i∈{0,1,…,N-1}; TP will S i The single photons are sent one by one to the semi-quantum participant P i ;Except for the first single photon, TP will send the next single photon only after receiving the previous single photon; S2) When receiving S i When a single photon is generated, the half-quantum participant P i After randomly performing CTRL or SITF operations on it, it is sent to the semi-quantum participant P. (i+1)modN ; Here, CTRL operation means no interference to single photons, and SITF operation means using The basis measures a single photon and prepares a new single photon in the same state; i P i The single photon sequences formed after SIFT operation and CTRL operation are respectively denoted as S i SIFT sequence and S i CTRL sequence; here, i∈{0,1,…,N-1}; S3) When receiving the message from P i When a single photon is emitted, P (i+1)modN Perform SIFT or unitary operations on it randomly (i.e. ) and then sent to TP; i SIFT sequence is transformed into (i+1)modN The sequences formed after SIFT operation and unitary operation are respectively denoted as S i SIFTSIFT sequence and S i SIFTU sequence, S i CTRL sequence via P (i+1)modN The sequences formed after SIFT operation and unitary operation are respectively denoted as S i CTRLSIFT sequence and S i CTRLU sequence; here, i∈{0,1,…,N-1}, k,l∈{0,1}; S4) For TP-P i -P (i+1)modN -TP loop, TP from S i Random selection single photon and publish the corresponding position, and require P i and P (i+1)modN Publish the corresponding operation and measurement results, and finally select the correct measurement basis shown in Table 1 to measure the received single photon; when P i The CTRL operation is selected and P (i+1)modN When the unitary operation is selected, TP i The initial preparation state of the selected single photon, P (i+1)modN For S i The unitary operation applied by the corresponding single photon in the CTRL sequence and the use of the prepared basis pairs from P (i+1)modN Received S i The error rate is calculated from the measurement results of the corresponding single photons in the CTRLU sequence; when P i SIFT operation is selected and P (i+1)modN When the unitary operation is selected, TP i The initial preparation state of the selected single photon, P i For S i The single photon selected Base measurement results, P (i+1)modN For S i The unitary operation applied to the corresponding single photon in the SIFT sequence and its own (i+1)modN Received S i The corresponding single photon in the SIFTU sequence The error rate is calculated based on the measurement results; when P i The CTRL operation is selected and P (i+1)modN When SIFT operation is selected, TP i The initial preparation state of the selected single photon, P (i+1)modN For S i The corresponding single photon in the CTRL sequence The base measurement results and the (i+1)modN Received S i The corresponding single photon in the CTRLSIFT sequence The error rate is calculated based on the measurement results; when P i SIFT operation is selected and P (i+1)modN When SIFT operation is selected, TP i The initial preparation state of the selected single photon, P i For S i The single photon selected Base measurement results, P (i+1)modN For S i The corresponding single photon in the SIFT sequence The base measurement results and the (i+1)modN Received S i The corresponding single photon in the SIFT sequence The error rate is calculated based on the measurement results; if any error rate is unreasonably large, TP will consider the quantum channel unsafe and terminate the communication early; in addition, if i The proportion of SIFT operations in the published operations is unreasonably high,,and the communication will be terminated prematurely;,Here,i∈{0,1,…,N-1}; Table 1 In TP-P i -P (i+1)modN Correct measurement basis for TP in the loop S5) For TP-P i -P (i+1)modN -TP loop, in order to detect whether TP is loyal, P i From S i Random selection The single photon is published and the corresponding position is announced, and then TP is required to announce the S i The initial preparation state of the selected single photon; if TP is Base preparation i Selected S i single photon, TP will randomly use Base or Base measurement from P (i+1)modN The corresponding single photon received; if TP is Base preparation i Selected S i single photon, TP will randomly use Base or Base measurement from P (i+1)modN The corresponding single photon received; P i TP is required to publish measurement results; there are six situations: Situation ①: P i Select SIFT operation, P (i+1)modN Select any one of SIFT operation and unitary operation, while TP selects In this case, TP is measured on Base preparation i Selected S i single photon; P i With P (i+1)modN According to my own operation and measurement results and the initial preparation state and Z published by TP P (Z S ) to calculate the error rate based on the measurement results; Situation ②: P i Select SIFT operation, P (i+1)modN Select any one of SIFT operation and unitary operation, while TP selects In this case, TP can be measured with It is possible that Base preparation i Selected S i single photon; when TP is Base preparation i Selected S i When a single photon is emitted, P i With P (i+1)modN According to my own operation and measurement results and the initial preparation state and The error rate of the base measurement results calculation; Situation ③:P i Select the CTRL operation, P (i+1)modN The unitary operation is selected, while TP selects In this case, TP is measured on Base preparation i Selected S i single photon; P i With P (i+1)modN According to your own operation and the initial preparation state and The error rate of the base measurement results calculation; Situation ④: P i Select the CTRL operation, P (i+1)modN The unitary operation is selected, while TP selects In this case, TP can be measured with It is possible that Base preparation i Selected S i single photon; when TP is Base preparation i Selected S i When a single photon is emitted, P i With P (i+1)modN According to my own operation and the initial preparation state and Z published by TP P (Z S ) to calculate the error rate based on the measurement results; Situation ⑤:P i Select the CTRL operation, P (i+1)modN The SIFT operation was selected, while TP selected In this case, TP is measured on Base preparation i Selected S i single photon; P i With P (i+1)modN According to my own operation and measurement results and the initial preparation state and Z published by TP P (Z S ) Calculate the error rate based on the measurement results; Situation 6: P i Select the CTRL operation, P (i+1)modN The SIFT operation was selected, while TP selected In this case, TP can be measured with It is possible that Base preparation i Selected S i single photon; when TP is Base preparation i Selected S i When a single photon is emitted, P i With P (i+1)modN According to your own operation and the initial preparation state and The error rate is calculated based on the measurement results; If the error rate of any of the above six situations is unreasonably large, P i and P (i+1)modN The TP will be considered disloyal and communication will be terminated prematurely; Here, i∈{0,1,…,N-1}; S6) For TP-P i -P (i+1)modN -S in TP loop i The remaining 4n single photons, P i and P (i+1)modN Publish the types of operations imposed separately; TP to P (i+1)modN Received S i The corresponding remaining single photons in the SIFTU sequence are Base measurement, and publish their own S i The initial preparation basis of the corresponding single photon in Base preparation S i When the corresponding single photon in S (Z P )Base measurement results; TP to S i The initial prepared state of the corresponding single photon is represented as |φ>, and the polarization state and empty mode of |φ> are represented as |S i P> and |S i S>,P i Yes | i P> and |S i The measurement results of S> are expressed as |S i SIFTP> and |S i SIFTS>,P (i+1)modN Yes | i SIFTP> and |S i The unitary operations applied by SIFTS> are denoted as S i U P and S i U S ,TP to P (i+1)modN Received S i U P |S i SIFTP> and S i U S |S i The measurement results of SIFTS> are represented as |S i TPP> and |S i TPS>; If the initial preparation base of TP is The following relationship will exist: If the initial preparation base of TP is The following relationship will exist: In this way, P i and P (i+1)modN Can be easily shared by E(|S i _SITF_S>) and E(|S i _SITF_P>) i((i+1)modN) , where K i((i+1)modN) The length of is n bits, that is here, TP selects the correct measurement basis pair from P (i+1)modN Received S i The corresponding remaining single photons in the CTRLU sequence are measured and their own responses to S are announced. i The initial preparation basis of the corresponding single photon in TP i The initial preparation state of the corresponding single photon in is expressed as The polarization state and empty mode of are represented as |S i _P'> and |S i _S'>,P (i+1)modN Yes | i _P'> and |S i The unitary operations applied by _S'> are denoted as S i _U' P and S i _U' S ,TP to P (i+1)modN Received S i _U' P |S i _P'> and S i _U' S |S i The measurement results of |S i _TP_P'> and |S i _TP_S'>; If the initial preparation base of TP is The following relationship will exist: If the initial preparation base of TP is The following relationship will exist: Therefore, P (i+1)modN and TP can be easily shared by E(S i U' P ) and E(S i U' S ) composed of a key K T((i+1)modN) , where K T((i+1)modN) The length of is n bits, that is Here, i∈{0,1,…,N-1}.

Images