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基于高维单粒子态的双向半量子安全直接通信协议

龚黎华 陈振泳 徐良超 周南润

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基于高维单粒子态的双向半量子安全直接通信协议

龚黎华, 陈振泳, 徐良超, 周南润

Bi-directional semi-quantum secure direct communication protocol based on high-dimensional single-particle states

Gong Li-Hua, Chen Zhen-Yong, Xu Liang-Chao, Zhou Nan-Run
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  • 本文设计了一个基于高维单粒子态的双向半量子安全直接通信协议, 该协议包括量子方Alice和经典方Bob, 每个参与方可以同时接收和发送秘密信息. 协议中的经典方Bob无需具备量子态检测能力, 因此该协议在现有技术条件下更易实现. 安全性分析表明: 在不被合法通信者发现的情况下, 截获重发、测量重发、篡改攻击以及纠缠攻击等常见攻击手段均无法获取秘密信息. 此外, 该协议利用高维单粒子态作为信息传输的载体, 这有效提高了秘密信息的传输效率.
    Semi-quantum secure direct communication allows the quantum party and the classical party to transmit secure messages directly, but does not need sharing a secret key in advance. To increase the information transmission efficiency and practicability of semi-quantum secure direct communication, a bidirectional semi-quantum secure direct communication protocol with high-dimensional single-particle states is designed. The proposed protocol involves quantum party Alice and classical party Bob. Each participant can receive a secret message while sending a secret message. Unlike most of existing quantum secure direct communication protocols, it is not necessary for the classical party Bob in the proposed protocol to possess the capability of measuring quantum states, which greatly enhances the feasibility of the protocol. The protocol allows the classical party Bob to implement the unitary operations on particles and reorder the quantum sequence. Furthermore, the quantum party Alice and the classical party Bob can verify the correctness of the received secret message with the Hash function. Security analysis indicates that without being discovered by the legitimate participants, Eve cannot obtain the secret message with common attack, such as intercept-resend attack, measure-resend attack, tampering attack and entanglement-measure attack. Compared with the typical semi-quantum secure direct communication protocols, the proposed protocol has a high qubit efficiency of about 28.6%. In addition, the transmission efficiency of secret message is greatly enhanced, since the proposed protocol utilizes the high-dimensional single-particle states as the carrier of secret message.
      通信作者: 周南润, znr21@163.com
    • 基金项目: 国家自然科学基金(批准号: 61871205)资助的课题.
      Corresponding author: Zhou Nan-Run, znr21@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61871205).
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    Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895Google Scholar

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    Li X H, Ghose S 2015 Phys. Rev. A 91 012320Google Scholar

    [3]

    杨璐, 马鸿洋, 郑超, 丁晓兰, 高健存, 龙桂鲁 2017 物理学报 66 230303Google Scholar

    Yang L, Ma H Y, Zheng C, Ding X L, Gao J C, Long G L 2017 Acta Phys. Sin. 66 230303Google Scholar

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    Vlachou C, Krawec W, Mateus P, Paunković N, Souto A 2018 Quantum Inf. Process. 17 288Google Scholar

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    吴承峰, 杜亚男, 王金东, 魏正军, 秦晓娟, 赵峰, 张智明 2016 物理学报 65 100302Google Scholar

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    冯艳艳, 施荣华, 石金晶, 郭迎 2019 物理学报 68 120302Google Scholar

    Feng Y Y, Shi R H, Shi J J, Guo Y 2019 Acta Phys. Sin. 68 120302Google Scholar

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    荣民希, 辛向军, 李发根 2020 物理学报 69 190302Google Scholar

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    张沛, 周小清, 李智伟 2014 物理学报 63 130301Google Scholar

    Zhang P, Zhou X Q, Li Z W 2014 Acta Phys. Sin. 63 130301Google Scholar

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    Chen F L, Zhang H, Chen S G, Cheng W T 2021 Quantum Inf. Process. 20 178Google Scholar

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    Jiang D H, Tang K K, Xu G B 2021 Int. J. Theor. Phys. 60 4122Google Scholar

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    Ma Z H, Chen J Y, Li Z, Tang C, Sua Y M, Fan H, Huang Y P 2020 Phys. Rev. Lett. 125 263602Google Scholar

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    Wang Q Q, Zheng Y, Zhai C H, Li X D, Gong Q H, Wang J W 2021 J. Semicond. 42 091901Google Scholar

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    Long G L, Liu X S 2002 Phys. Rev. A 65 032302Google Scholar

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    Boström K, Felbinger T 2002 Phys. Rev. Lett. 89 187902Google Scholar

    [16]

    Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317Google Scholar

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    Deng F G, Long G L 2004 Phys. Rev. A 69 052319Google Scholar

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    Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305Google Scholar

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    Shi J, Gong Y X, Xu P, Zhu S N, Zhan Y B 2011 Commun. Theor. Phys. 56 831Google Scholar

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    郑晓毅 龙银香 2017 物理学报 66 180303Google Scholar

    Zheng X Y, Long Y X 2017 Acta Phys. Sin. 66 180303Google Scholar

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    Chen S S, Zhou L, Zhong W, Sheng Y B 2018 Sci. Chin. -Phys. Mech. Astron. 61 90312Google Scholar

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    Gao Z K, Li T, Li Z H 2019 EPL 125 40004Google Scholar

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    Zhou L, Sheng Y B, Long G L 2020 Sci. Bull. 65 12Google Scholar

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    Sheng Y B, Zhou L, Long G L 2022 Sci. Bull. 67 367Google Scholar

    [25]

    Hu J Y, Yu B, Jing M Y, Xiao L T, Jia S T, Qin G Q, Long G L 2016 Light Sci. Appl. 5 e16144Google Scholar

    [26]

    Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501Google Scholar

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    Zhu F, Zhang W, Sheng Y B, Huang Y D 2017 Sci. Bull. 62 1519Google Scholar

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    Qi Z T, Li Y H, Huang Y W, Feng J, Zheng Y L, Chen X F 2021 Light Sci. Appl. 10 183Google Scholar

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    Boyer M, Kenigsberg D, Mor T 2007 Phys. Rev. Lett. 99 140501Google Scholar

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    Zhou N R, Zhu K N, Bi W, Gong L H 2019 Quantum Inf. Process. 18 197Google Scholar

    [31]

    Tsai C W, Yang C W 2021 Sci. Rep. 11 23222Google Scholar

    [32]

    Han S Y, Huang Y T, Mi S, Qin X J, Wang J D, Yu Y F, Wei Z J, Zhang Z M 2021 EPJ Quantum Technol. 8 28Google Scholar

    [33]

    Jiang S Q, Zhou R G, Hu W W 2021 Int. J. Theor. Phys. 60 3353Google Scholar

    [34]

    Zhou N R, Xu Q D, Du N S, Gong L H 2021 Quantum Inf. Process. 20 124Google Scholar

    [35]

    Ye C Q, Li J, Chen X B, Yuan T 2021 Quantum Inf. Process. 20 262Google Scholar

    [36]

    Zou X F, Qiu D W 2014 Sci. Chin. -Phys. Mech. Astron. 57 1696Google Scholar

    [37]

    Gu J, Lin P H, Hwang T 2018 Quantum Inf. Process. 17 182Google Scholar

    [38]

    Zhang M H, Li H F, Xia Z Q, Feng X Y, Peng J Y 2017 Quantum Inf. Process. 16 117Google Scholar

    [39]

    Xie C, Li L Z, Situ H Z, He J H 2018 Int. J. Theor. Phys. 57 1881Google Scholar

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    Sun Y H, Yan L L, Chang Y, Zhang S B, Shao T T, Zhang Y 2019 Mod. Phys. Lett. A 34 1950004

    [41]

    Rong Z B, Qiu D W, Zou X F 2020 Int. J. Theor. Phys. 59 1807Google Scholar

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    Ye C Q, Ye T Y, He D, Gan Z G 2019 Int. J. Theor. Phys. 58 3797Google Scholar

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    Wen X J, Zhao X Q, Gong L H, Zhou N R 2019 Laser Phys. Lett. 16 075206Google Scholar

  • 图 1  窃听检测概率

    Fig. 1.  Eavesdropping detection probability.

    图 2  单粒子传输秘密信息-维数

    Fig. 2.  Single particle transport secret information - dimension.

    表 1  操作后粒子的分类

    Table 1.  Classification of the particles after operation.

    原始状态所属基Bob的操作标记为
    $\overline Z $CTRL$\overline Z - {\text{CTRL}}$
    $\overline Z $${U_m}$$\overline Z - U$
    $\overline X $CTRL$\overline X - {\text{CTRL}}$
    $\overline X $${U_m}$$\overline X - U$
    下载: 导出CSV

    表 2  Alice的窃听检测策略

    Table 2.  Eavesdropping detection strategy for Alice.

    原始状态Bob的操作Alice的操作预期结果
    $\left| k \right\rangle $CTRL$\overline Z $基测量$\left| k \right\rangle $
    $\left| k \right\rangle $${U_m}$$\overline Z $基测量$\left| {k \oplus m} \right\rangle $
    $F\left| k \right\rangle $CTRL$\overline X $基测量$F\left| k \right\rangle $
    $F\left| k \right\rangle $${U_m}$$\overline X $基测量$F\left| k \right\rangle $
    下载: 导出CSV

    表 3  Eve的截获重发攻击

    Table 3.  Intercept-resend attack by Eve.

    Alice发送的粒子Bob的操作Eve的操作Alice的操作窃听是否会被发现
    $\overline Z $CTRLCTRL用$\overline Z $基测量
    $\overline Z $CTRL${U_m}$用$\overline Z $基测量
    $\overline Z $${U_m}$CTRL用$\overline Z $基测量$\dfrac{ {d - 1} }{ {2 d} }$的概率被发现
    $\overline Z $${U_m}$${U_m}$用$\overline Z $基测量$\dfrac{ {d - 1} }{ {2 d} }$的概率被发现
    $\overline X $CTRLCTRL用$\overline X $基测量
    $\overline X $CTRL${U_m}$用$\overline X $基测量
    $\overline X $${U_m}$CTRL用$\overline X $基测量
    $\overline X $${U_m}$${U_m}$用$\overline X $基测量
    下载: 导出CSV

    表 4  Eve的测量重发攻击

    Table 4.  Measurement-resend attack by Eve.

    Alice发送的粒子Eve的测量基Bob得到的粒子Bob的操作Alice的操作窃听是否被发现
    $\overline Z $$\overline Z $$\overline Z $CTRL$\overline Z $基测量
    $\overline Z $$\overline Z $$\overline Z $${U_m}$$\overline Z $基测量
    $\overline Z $$\overline X $$\overline X $CTRL$\overline Z $基测量$\dfrac{ {d - 1} }{d}$概率被发现
    $\overline Z $$\overline X $$\overline X $${U_m}$$\overline Z $基测量$\dfrac{ {d - 1} }{ {2 d} }$概率被发现
    $\overline X $$\overline Z $$\overline Z $CTRL$\overline X $基测量$\dfrac{ {d - 1} }{d}$概率被发现
    $\overline X $$\overline Z $$\overline Z $${U_m}$$\overline X $基测量$\dfrac{ {d - 1} }{d}$概率被发现
    $\overline X $$\overline X $$\overline X $CTRL$\overline X $基测量
    $\overline X $$\overline X $$\overline X $${U_m}$$\overline X $基测量
    下载: 导出CSV

    表 5  本协议与现有经典SQSDC协议的比较

    Table 5.  Comparison of the proposed protocol with existing classical SQSDC protocols.

    协议文献[36]文献[38]协议一[40]协议二[40]本文协议
    量子载体二维单粒子态二维Bell态二维Bell态二维Bell态$d$维单粒子态
    通信模式单向单向单向单向双向
    经典方是否
    需要测量能力
    每粒子传输秘密信息(bit)1111${\log _2}d$
    量子通信协议效率(%)14.319.016.728.628.6
    下载: 导出CSV
  • [1]

    Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895Google Scholar

    [2]

    Li X H, Ghose S 2015 Phys. Rev. A 91 012320Google Scholar

    [3]

    杨璐, 马鸿洋, 郑超, 丁晓兰, 高健存, 龙桂鲁 2017 物理学报 66 230303Google Scholar

    Yang L, Ma H Y, Zheng C, Ding X L, Gao J C, Long G L 2017 Acta Phys. Sin. 66 230303Google Scholar

    [4]

    Vlachou C, Krawec W, Mateus P, Paunković N, Souto A 2018 Quantum Inf. Process. 17 288Google Scholar

    [5]

    吴承峰, 杜亚男, 王金东, 魏正军, 秦晓娟, 赵峰, 张智明 2016 物理学报 65 100302Google Scholar

    Wu C F, Du Y N, Wang J D, Wei Z J, Qin X J, Zhao F, Zhang Z M 2016 Acta Phys. Sin. 65 100302Google Scholar

    [6]

    安雪碧, 银振强, 韩正甫 2015 物理学报 64 140303Google Scholar

    An X B, Yin Z Q, Han Z F 2015 Acta Phys. Sin. 64 140303Google Scholar

    [7]

    冯艳艳, 施荣华, 石金晶, 郭迎 2019 物理学报 68 120302Google Scholar

    Feng Y Y, Shi R H, Shi J J, Guo Y 2019 Acta Phys. Sin. 68 120302Google Scholar

    [8]

    荣民希, 辛向军, 李发根 2020 物理学报 69 190302Google Scholar

    Rong M X, Xin X J, Li F G 2020 Acta Phys. Sin. 69 190302Google Scholar

    [9]

    张沛, 周小清, 李智伟 2014 物理学报 63 130301Google Scholar

    Zhang P, Zhou X Q, Li Z W 2014 Acta Phys. Sin. 63 130301Google Scholar

    [10]

    Chen F L, Zhang H, Chen S G, Cheng W T 2021 Quantum Inf. Process. 20 178Google Scholar

    [11]

    Jiang D H, Tang K K, Xu G B 2021 Int. J. Theor. Phys. 60 4122Google Scholar

    [12]

    Ma Z H, Chen J Y, Li Z, Tang C, Sua Y M, Fan H, Huang Y P 2020 Phys. Rev. Lett. 125 263602Google Scholar

    [13]

    Wang Q Q, Zheng Y, Zhai C H, Li X D, Gong Q H, Wang J W 2021 J. Semicond. 42 091901Google Scholar

    [14]

    Long G L, Liu X S 2002 Phys. Rev. A 65 032302Google Scholar

    [15]

    Boström K, Felbinger T 2002 Phys. Rev. Lett. 89 187902Google Scholar

    [16]

    Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317Google Scholar

    [17]

    Deng F G, Long G L 2004 Phys. Rev. A 69 052319Google Scholar

    [18]

    Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305Google Scholar

    [19]

    Shi J, Gong Y X, Xu P, Zhu S N, Zhan Y B 2011 Commun. Theor. Phys. 56 831Google Scholar

    [20]

    郑晓毅 龙银香 2017 物理学报 66 180303Google Scholar

    Zheng X Y, Long Y X 2017 Acta Phys. Sin. 66 180303Google Scholar

    [21]

    Chen S S, Zhou L, Zhong W, Sheng Y B 2018 Sci. Chin. -Phys. Mech. Astron. 61 90312Google Scholar

    [22]

    Gao Z K, Li T, Li Z H 2019 EPL 125 40004Google Scholar

    [23]

    Zhou L, Sheng Y B, Long G L 2020 Sci. Bull. 65 12Google Scholar

    [24]

    Sheng Y B, Zhou L, Long G L 2022 Sci. Bull. 67 367Google Scholar

    [25]

    Hu J Y, Yu B, Jing M Y, Xiao L T, Jia S T, Qin G Q, Long G L 2016 Light Sci. Appl. 5 e16144Google Scholar

    [26]

    Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501Google Scholar

    [27]

    Zhu F, Zhang W, Sheng Y B, Huang Y D 2017 Sci. Bull. 62 1519Google Scholar

    [28]

    Qi Z T, Li Y H, Huang Y W, Feng J, Zheng Y L, Chen X F 2021 Light Sci. Appl. 10 183Google Scholar

    [29]

    Boyer M, Kenigsberg D, Mor T 2007 Phys. Rev. Lett. 99 140501Google Scholar

    [30]

    Zhou N R, Zhu K N, Bi W, Gong L H 2019 Quantum Inf. Process. 18 197Google Scholar

    [31]

    Tsai C W, Yang C W 2021 Sci. Rep. 11 23222Google Scholar

    [32]

    Han S Y, Huang Y T, Mi S, Qin X J, Wang J D, Yu Y F, Wei Z J, Zhang Z M 2021 EPJ Quantum Technol. 8 28Google Scholar

    [33]

    Jiang S Q, Zhou R G, Hu W W 2021 Int. J. Theor. Phys. 60 3353Google Scholar

    [34]

    Zhou N R, Xu Q D, Du N S, Gong L H 2021 Quantum Inf. Process. 20 124Google Scholar

    [35]

    Ye C Q, Li J, Chen X B, Yuan T 2021 Quantum Inf. Process. 20 262Google Scholar

    [36]

    Zou X F, Qiu D W 2014 Sci. Chin. -Phys. Mech. Astron. 57 1696Google Scholar

    [37]

    Gu J, Lin P H, Hwang T 2018 Quantum Inf. Process. 17 182Google Scholar

    [38]

    Zhang M H, Li H F, Xia Z Q, Feng X Y, Peng J Y 2017 Quantum Inf. Process. 16 117Google Scholar

    [39]

    Xie C, Li L Z, Situ H Z, He J H 2018 Int. J. Theor. Phys. 57 1881Google Scholar

    [40]

    Sun Y H, Yan L L, Chang Y, Zhang S B, Shao T T, Zhang Y 2019 Mod. Phys. Lett. A 34 1950004

    [41]

    Rong Z B, Qiu D W, Zou X F 2020 Int. J. Theor. Phys. 59 1807Google Scholar

    [42]

    Ye C Q, Ye T Y, He D, Gan Z G 2019 Int. J. Theor. Phys. 58 3797Google Scholar

    [43]

    Wen X J, Zhao X Q, Gong L H, Zhou N R 2019 Laser Phys. Lett. 16 075206Google Scholar

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  • 收稿日期:  2021-09-12
  • 修回日期:  2022-03-14
  • 上网日期:  2022-07-12
  • 刊出日期:  2022-07-05

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