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一种基于标记单光子源的态制备误差容忍量子密钥分发协议

马啸 孙铭烁 刘靖阳 丁华建 王琴

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一种基于标记单光子源的态制备误差容忍量子密钥分发协议

马啸, 孙铭烁, 刘靖阳, 丁华建, 王琴

State preparation error tolerant quantum key distribution protocol based on heralded single photon source

Ma Xiao, Sun Ming-Shuo, Liu Jing-Yang, Ding Hua-Jian, Wang Qin
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  • 在实际量子密钥分发系统中, 由于设备、器件存在缺陷, 在量子态制备过程中往往存在误差, 而这些态制备误差会导致一定的系统安全性漏洞. 本文在Tamaki等(Phys. Rev. A 90 052314)的工作基础之上, 提出了一种基于标记单光子源的态制备误差容忍量子密钥分发协议. 本文将发送端制备态误差进行参数刻画并带入量子密钥协议安全性分析之中, 避免了实际应用中由于态制备装置的不理想可能引入的安全性漏洞, 提高了系统的安全性. 同时, 为了方便起见, 本文采用三强度诱骗态方案开展建模分析与数值仿真计算. 仿真结果显示, 本文提出的协议对态制备误差具有很好的鲁棒性. 同时, 由于标记单光子源具有真空脉冲概率低的优点, 与此前基于弱相干态脉冲的同类协议相比, 我们的协议在传输距离较远时能够显示出更优的性能. 因而, 该工作有望为未来发展长距离量子保密通信应用与研究提供重要的参考价值.
    In practical quantum key distribution systems, there inevitably exist errors in the quantum state preparation process due to imperfections in realistic equipment and devices. Those errors would lead to some security loopholes in the quantum key distribution systems. According to the work of Tamaki et al. (Phys. Rev. A 90 052314), here in this work we propose a state preparation error tolerant quantum key distribution protocol through using heralded single-photon sources.  In this protocol, we characterize the size of the error in the preparation state of Alice and bring it into the security analysis, thereby avoiding possible security loopholes and improving the security of the system. Moreover, we take the three-intensity decoy-state method for example to introduce the method of constructing the model and estimating the parameters, and carry out corresponding numerical simulations.  We make a comparison between the loss tolerant protocol with weak coherent source (WCS) and our present protocol using heralded single-photon source (HSPS). Simulation results show that under the same state preparation error, the key generation rate of the protocol based on WCS is higher than that of protocol based on HSPS at short transmission distances (e.g. less than 150 km). The main reason is that the detection efficiency of the local detector used in the latter scheme is low. However, in the case of long transmission distances (e.g. greater than 200 km), the key generation rate of scheme with WCS drops deeply, while the decline of the key generation rate of the present scheme is much flatter. As a result, the former can no longer generate keys after 211 km, while the latter can transmit a maximum distance of 228 km.  Moreover, we also make a comparison between the present scheme and the GLLP protocol with HSPS. The simulation results show that the GLLP protocol with HSPS is very sensitive to the state preparation error and its key generation rate will rapidly decrease with the increase of the state preparation error. On the contrary, our present protocol shows almost no performance degradation under practical state preparation errors. It thus verify the robustness against the state preparation errors of our present work.  In addition, in principle, the method can also be combined with the measurement-device-independent quantum key distribution protocol and the twin-field quantum key distribution protocol to further increase the secure communication transmission distance that the present system can reach. Therefore, this work may provide an important reference value for the practical application of long-distance quantum secure communication in the near future.
      通信作者: 王琴, qinw@njupt.edu.cn
    • 基金项目: 国家重点研发计划 (批准号: 2018YFA0306400, 2017YFA0304100)、国家自然科学基金(批准号: 12074194, 11774180)、江苏省自然科学基金前沿技术项目(批准号: BK20192001)和江苏省研究生科研创新计划(批准号: KYCX20_0726, KYCX19_0951)资助的课题
      Corresponding author: Wang Qin, qinw@njupt.edu.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant Nos. 2018YFA0306400, 2017YFA0304100), the National Natural Science Foundation of China (Grant Nos. 12074194, 11774180), the Leading-edge Technology Program of Jiangsu Natural Science Foundation, China (Grant No. BK20192001), and the Postgraduate Scientific Research & Innovation Program of Jiangsu Province, China (Grant Nos. KYCX20_0726, KYCX19_0951)
    [1]

    Bennett C H, Brassard G 1984 Proceedings of IEEE International Conference on Computers, System and Signal Processing (Vol. 1 of 3) (Bangalore: IEEE) p175

    [2]

    Shor P W, Preskill J 2000 Phys. Rev. Lett. 85 441Google Scholar

    [3]

    Mayers D 2001 J. ACM 48 351Google Scholar

    [4]

    Lo H K, Chau H F 1999 Science 283 2050Google Scholar

    [5]

    Brassard G, Lütkenhaus N, Mor T, Sanders B C 2000 Phys. Rev. Lett. 85 1330Google Scholar

    [6]

    Shannon C E 1949 Bell Syst. Tech. J. 28 656Google Scholar

    [7]

    Gottesman D, Lo H K, Lütkenhaus N, Preskill J 2004 Quantum Inf. Comput. 4 325

    [8]

    Tamaki K, Curty M, Kato G, Lo H K, Azuma K 2014 Phys. Rev. A 90 052314Google Scholar

    [9]

    Xu F H, Wei K J, Sajeed S H, Kaiser S, Sun S H, Tang Z Y, Qian L, Makarov V, Lo H K 2015 Phys. Rev. A. 92 032305Google Scholar

    [10]

    Tang Z Y, Wei K J, Bedroya O, Qian L, Lo H K 2016 Phys. Rev. A. 93 042308Google Scholar

    [11]

    Wang J P, Liu H W, Ma H Q, Sun S H 2019 Phys. Rev. A 99 032309Google Scholar

    [12]

    Yin Z Q, Fung C H F, Ma X F, Zhang C M, Li H W, Chen W, Wang S, Guo G C, Han Z F 2013 Phys. Rev. A 88 062322Google Scholar

    [13]

    Zhou X Y, Zhang C M, Guo G C, Wang Q 2019 IEEE Photonics J. 11 7600207Google Scholar

    [14]

    Zhou X Y, Ding H J, Zhang C H, Li J, Zhang C M, Wang Q 2020 Opt. Lett. 45 4176Google Scholar

    [15]

    Pereira M, Curty M, Tamaki K 2019 npj Quantum Inf. 5 62Google Scholar

    [16]

    Wang X B 2005 Phys. Rev. Lett. 94 230503Google Scholar

    [17]

    Lo H K, Ma X F, Chen K 2005 Phys. Rev. Lett. 94 230504Google Scholar

    [18]

    Riedmatten H D, Scarani V, Marcikic I, Acín A, Tittel W, Zbinden H, Gisin N 2004 J. Mod. Opt. 51 1637Google Scholar

    [19]

    Ljunggren D, Tengner M 2005 Phys. Rev. A 72 062301Google Scholar

    [20]

    Castelletto S, Degiovanni I P, Schettini V, Migdall A 2005 Opt. Express 13 6709Google Scholar

    [21]

    Pittmann T B, Jacobs B C, Franson J D 2005 Opt. Commun. 246 545Google Scholar

    [22]

    Mori S, Söderholm J, Namekata N, Inoue S 2006 Opt. Commun. 264 156Google Scholar

    [23]

    朱峰, 王琴 2014 光学学报 34 0627002

    Zhu F, Wang Q 2014 Acta Opt. Sin. 34 0627002

    [24]

    Wang Q, Wang X B, Guo G C 2007 Phys. Rev. A 75 012312Google Scholar

    [25]

    Wang Q, Chen W, Xavier G, et al. 2008 Phys. Rev. Lett. 100 090501Google Scholar

    [26]

    Lütkenhaus N 2000 Phys. Rev. A 61 052304Google Scholar

    [27]

    Zhou Y H, Yu Z W, Wang X B 2016 Phys. Rev. A 93 042324Google Scholar

    [28]

    Zhang C H, Zhang C M, Guo G C, Wang Q 2018 Opt. Express 26 4219Google Scholar

    [29]

    Zhou X Y, Zhang C H, Zhang C M, Wang Q 2017 Phys. Rev. A 96 052337Google Scholar

    [30]

    Jiang C, Yu Z W, Hu X L, Wang X B 2021 Phys. Rev. A 103 012402Google Scholar

    [31]

    Lucamarini M, Yuan Z L, Dynes J F, Shields A J 2018 Nature 557 400Google Scholar

    [32]

    Ma X F, Zeng P, Zhou H Y 2019 Phys. Rev. X 9 029901Google Scholar

    [33]

    Wang X B, Yu Z W, Hu X L 2018 Phys. Rev. A. 98 062323Google Scholar

    [34]

    Cui C H, Yin Z Q, Wang R, et al. 2019 Phys. Rev. Appl. 11 034053Google Scholar

  • 图 1  实际系统中的标记单光子源的光路装置模型

    Fig. 1.  Model of optical path device for marking single photon source in experimental system.

    图 2  基于不同光源的态制备误差容忍协议密钥生成率对比图

    Fig. 2.  Comparison of the key generation rates of the two different state-preparation-error tolerant protocols using either HSPS or WCS.

    图 3  在不同态制备误差下, 对比本协议与GLLP协议[24]的密钥生成率随传输距离变化趋势

    Fig. 3.  Comparison of the key generation rate between the present work and GLLP protocol under different state preparation errors.

    表 1  在平均光子数强度为0.4时, WCS和HSPS光源中不同光子数脉冲出现的概率

    Table 1.  Proportion of different photon number pulses in WCS and HSPS when the average photon intensity is 0.4.

    光源类型光子分布
    真空态单光子多光子
    WCS0.7432180.2217460.035036
    HSPS7.432 × 10–70.4546830.545316
    下载: 导出CSV

    表 2  基于HSPS的三强度诱骗态态制备误差容忍QKD协议仿真使用的参数列表

    Table 2.  Parameter list used in simulation of state-preparation-error tolerant QKD protocol for three strength decoy states based on HSPS.

    Bob探测器暗
    计数率$ {d_{\rm{B}}} $
    Bob探测器
    效率$ {\eta _{\rm{B}}} $
    系统纠错
    系数$ f $
    Alice探测器暗
    计数率$ {d_{\rm{A}}} $
    Alice探测器探
    测效率$ {\eta _A} $
    信道损耗
    系数$ \alpha $/(dB·km–1)
    0.5 × 10–60.151.2210–60.750.2
    下载: 导出CSV
  • [1]

    Bennett C H, Brassard G 1984 Proceedings of IEEE International Conference on Computers, System and Signal Processing (Vol. 1 of 3) (Bangalore: IEEE) p175

    [2]

    Shor P W, Preskill J 2000 Phys. Rev. Lett. 85 441Google Scholar

    [3]

    Mayers D 2001 J. ACM 48 351Google Scholar

    [4]

    Lo H K, Chau H F 1999 Science 283 2050Google Scholar

    [5]

    Brassard G, Lütkenhaus N, Mor T, Sanders B C 2000 Phys. Rev. Lett. 85 1330Google Scholar

    [6]

    Shannon C E 1949 Bell Syst. Tech. J. 28 656Google Scholar

    [7]

    Gottesman D, Lo H K, Lütkenhaus N, Preskill J 2004 Quantum Inf. Comput. 4 325

    [8]

    Tamaki K, Curty M, Kato G, Lo H K, Azuma K 2014 Phys. Rev. A 90 052314Google Scholar

    [9]

    Xu F H, Wei K J, Sajeed S H, Kaiser S, Sun S H, Tang Z Y, Qian L, Makarov V, Lo H K 2015 Phys. Rev. A. 92 032305Google Scholar

    [10]

    Tang Z Y, Wei K J, Bedroya O, Qian L, Lo H K 2016 Phys. Rev. A. 93 042308Google Scholar

    [11]

    Wang J P, Liu H W, Ma H Q, Sun S H 2019 Phys. Rev. A 99 032309Google Scholar

    [12]

    Yin Z Q, Fung C H F, Ma X F, Zhang C M, Li H W, Chen W, Wang S, Guo G C, Han Z F 2013 Phys. Rev. A 88 062322Google Scholar

    [13]

    Zhou X Y, Zhang C M, Guo G C, Wang Q 2019 IEEE Photonics J. 11 7600207Google Scholar

    [14]

    Zhou X Y, Ding H J, Zhang C H, Li J, Zhang C M, Wang Q 2020 Opt. Lett. 45 4176Google Scholar

    [15]

    Pereira M, Curty M, Tamaki K 2019 npj Quantum Inf. 5 62Google Scholar

    [16]

    Wang X B 2005 Phys. Rev. Lett. 94 230503Google Scholar

    [17]

    Lo H K, Ma X F, Chen K 2005 Phys. Rev. Lett. 94 230504Google Scholar

    [18]

    Riedmatten H D, Scarani V, Marcikic I, Acín A, Tittel W, Zbinden H, Gisin N 2004 J. Mod. Opt. 51 1637Google Scholar

    [19]

    Ljunggren D, Tengner M 2005 Phys. Rev. A 72 062301Google Scholar

    [20]

    Castelletto S, Degiovanni I P, Schettini V, Migdall A 2005 Opt. Express 13 6709Google Scholar

    [21]

    Pittmann T B, Jacobs B C, Franson J D 2005 Opt. Commun. 246 545Google Scholar

    [22]

    Mori S, Söderholm J, Namekata N, Inoue S 2006 Opt. Commun. 264 156Google Scholar

    [23]

    朱峰, 王琴 2014 光学学报 34 0627002

    Zhu F, Wang Q 2014 Acta Opt. Sin. 34 0627002

    [24]

    Wang Q, Wang X B, Guo G C 2007 Phys. Rev. A 75 012312Google Scholar

    [25]

    Wang Q, Chen W, Xavier G, et al. 2008 Phys. Rev. Lett. 100 090501Google Scholar

    [26]

    Lütkenhaus N 2000 Phys. Rev. A 61 052304Google Scholar

    [27]

    Zhou Y H, Yu Z W, Wang X B 2016 Phys. Rev. A 93 042324Google Scholar

    [28]

    Zhang C H, Zhang C M, Guo G C, Wang Q 2018 Opt. Express 26 4219Google Scholar

    [29]

    Zhou X Y, Zhang C H, Zhang C M, Wang Q 2017 Phys. Rev. A 96 052337Google Scholar

    [30]

    Jiang C, Yu Z W, Hu X L, Wang X B 2021 Phys. Rev. A 103 012402Google Scholar

    [31]

    Lucamarini M, Yuan Z L, Dynes J F, Shields A J 2018 Nature 557 400Google Scholar

    [32]

    Ma X F, Zeng P, Zhou H Y 2019 Phys. Rev. X 9 029901Google Scholar

    [33]

    Wang X B, Yu Z W, Hu X L 2018 Phys. Rev. A. 98 062323Google Scholar

    [34]

    Cui C H, Yin Z Q, Wang R, et al. 2019 Phys. Rev. Appl. 11 034053Google Scholar

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出版历程
  • 收稿日期:  2021-08-07
  • 修回日期:  2021-09-11
  • 上网日期:  2022-01-23
  • 刊出日期:  2022-02-05

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