搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

改进的测量设备无关协议参数优化方法

周江平 周媛媛 周学军

引用本文:
Citation:

改进的测量设备无关协议参数优化方法

周江平, 周媛媛, 周学军

Improved parameter optimization method for measurement device independent protocol

Zhou Jiang-Ping, Zhou Yuan-Yuan, Zhou Xue-Jun
PDF
HTML
导出引用
  • 实际量子密钥分发中参数的优化选择能大幅提升系统密钥生成率和最大传输距离, 由于全局搜索算法的成本过大, 本地搜索算法被广泛地应用. 然而该算法存在两个问题, 一是所得解不一定为全局最优解, 二是算法的有效性极大地受制于初始值的选择. 利用蒙特卡罗方法对密钥生成率函数是否为凸函数进行了证明, 并仿真分析了密钥生成率函数在不同参数维度上的特性, 提出了粒子群本地搜索算法并与本地搜索算法进行仿真比较. 结果表明, 密钥生成率函数为非凸函数, 但合理设置初始值, 本地搜索算法仍能求得全局最优解; 在传输距离较远时, 本地搜索算法因难以通过随机取值的方法得到有效的初始值而失效, 粒子群本地搜索算法能克服这一缺点, 以轻微增加算法复杂度为代价, 提升了系统的最大传输距离.
    The optimal selection of parameters in practical quantum key distribution can greatly improve the key generation rate and maximum transmission distance of the system. Owing to the high cost of global search algorithm, local search algorithm is widely used. However, there are two shortcomings in local search algorithm. One is that the solution obtained is not always the global optimal solution, and the other is that the effectiveness of the algorithm is greatly dependent on the choice of initial value. This paper uses the Monte Carlo method to prove whether the key generation rate function is convex, and also simulates and analyzes the projection of the key generation rate function on each dimension of the parameter, in contrast to the approach in previous article. In order to eliminate the effect of the initial value, this paper proposes the particle swarm local search optimization algorithm which integrates particle swarm optimization algorithm and local search algorithm. The first step is to use the particle swarm optimization to find a valid parameter which leads to nonzero key generation rate, and the second step is to adopt the parameter as the initial value of local search algorithm to derive the global optimal solution. Then, the two algorithms are used to conduct simulation and their results are compared. The results show that the key generation rate function is non-convex because it does not satisfy the definition of a convex function, however, since the key generation rate function has only one non-zero stagnation point, the LSA algorithm can still obtain the global optimal solution with an appropriate initial value. When the transmission distance is relatively long, the local search algorithm is invalid because it is difficult to obtain an effective initial value by random value method. The particle swarm optimization algorithm can overcome this shortcoming and improve the maximum transmission distance of the system at the cost of slightly increasing the complexity of the algorithm.
      通信作者: 周媛媛, EPJZYY@aliyun.com
      Corresponding author: Zhou Yuan-Yuan, EPJZYY@aliyun.com
    [1]

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

    [2]

    Pirandola S, Andersen U L, Banchi L, Berta M, Bunandar D, Colbeck R, Englund D, Gehring T, Lupo C, Ottaviani C, Pereira J L, Razavi M, Shamsul Shaari J, Tomamichel M, Usenko V C, Vallone G, Villoresi P, Wallden P 2020 Adv. Opt. Photonics 12 1012Google Scholar

    [3]

    Ekert A K 1991 Phys. Rev. Lett. 67 661Google Scholar

    [4]

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

    [5]

    Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002Google Scholar

    [6]

    Gerhardt I, Liu Q, Lamas-Linares A, Skaar J, Kurtsiefer C, Makarov V 2011 Nat. Commun. 2 349Google Scholar

    [7]

    Jain N, Stiller B, Khan I, Elser D, Marquardt C, Leuchs G 2016 Contemp. Phys. 57 366Google Scholar

    [8]

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

    [9]

    Lo H K, Curty M, Qi B 2012 Phys. Rev. Lett. 108 130503Google Scholar

    [10]

    Gu J, Cao X Y, Fu Y, He Z W, Yin Z J, Yin H L, Chen Z B 2022 Sci. Bull. 67 2167Google Scholar

    [11]

    Yin H L, Cao W F, Fu Y, Tang Y L, Liu Y, Chen T Y, Chen Z B 2014 Opt. Lett. 39 5451Google Scholar

    [12]

    Lo H K, Chau H F, Ardehali M 2005 J. Cryptol. 18 133Google Scholar

    [13]

    Wei Z, Wang W, Zhang Z, Gao M, Ma Z, Ma X 2013 Sci. Rep. 3 2453Google Scholar

    [14]

    Xu F, Xu H, Lo H K 2014 Phys. Rev. A 89 052333Google Scholar

    [15]

    Wang W, Lo H K 2019 Phys. Rev. A 100 062334Google Scholar

    [16]

    Ding H J, Liu J Y, Zhang C M, Wang Q 2020 Quantum Inf. Process. 19 60Google Scholar

    [17]

    Dong Q, Huang G, Cui W, Jiao R 2022 Quantum Inf. Process. 21 233Google Scholar

    [18]

    Dong Q, Huang G, Cui W, Jiao R 2021 Quantum Sci. Technol. 7 015014

    [19]

    Lu F Y, Yin Z Q, Wang C, Cui C H, Teng J, Wang S, Chen W, Huang W, Xu B J, Guo G C, Han Z F 2019 J. Opt. Soc. Am. B 36 B92Google Scholar

    [20]

    Boyd S P, Vandenberghe L 2004 Convex Optimization (New York: Cambridge University Press) p716

    [21]

    韩宝玲, 赵锐, 罗庆生, 徐峰, 赵嘉珩 2017 北京理工大学学报 37 461

    Han B L, Zhao R, Luo Q S, Xu F, Zhao J H 2017 J. Beijing Inst. Technol. 37 461

    [22]

    蒋丽, 叶润舟, 梁昌勇, 陆文星 2019 计算机工程与应用 55 130

    Jiang L, Ye R Z, Liang C Y, Lu W X 2019 Computer Engineering and Applications 55 130

    [23]

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

    [24]

    Ma X, Zeng P, Zhou H 2018 Phys. Rev. X 8 031043

    [25]

    Zhou L, Lin J, Jing Y, Yuan Z 2023 Nat. Commun. 14 928Google Scholar

    [26]

    Zeng P, Zhou H, Wu W, Ma X 2022 Nat. Commun. 13 3903Google Scholar

    [27]

    Xie Y M, Lu Y S, Weng C X, Cao X Y, Jia Z Y, Bao Y, Wang Y, Fu Y, Yin H L, Chen Z B 2022 PRX Quantum. 3 020315Google Scholar

    [28]

    Ma X, Fung C H F, Razavi M 2012 Phys. Rev. A 86 052305Google Scholar

    [29]

    Sun S H, Gao M, Li C Y, Liang L M 2013 Phys. Rev. A 87 052329Google Scholar

    [30]

    Ma X, Qi B, Zhao Y, Lo H K 2005 Phys. Rev. A 72 012326Google Scholar

    [31]

    Curty M, Xu F, Cui W, Lim C C W, Tamaki K, Lo H K 2014 Nat. Commun. 5 3732Google Scholar

    [32]

    Xu F, Curty M, Qi B, Lo H K 2013 New J. Phys. 15 113007Google Scholar

    [33]

    Yang X S 2021 Nature-Inspired Optimization Algorithms (London: Elsevier) pp111–113

    [34]

    Gandomi A H, Yun G J, Yang X S, Talatahari S 2013 Commun. Nonlinear Sci. Numer. Simul. 18 327Google Scholar

    [35]

    Ursin R, Tiefenbacher F, Schmitt-Manderbach T, et al. 2007 Nat. Phys. 3 481Google Scholar

  • 图 1  凸性判别函数$ F\left( {\theta , {{\boldsymbol{x}}_1}, {{\boldsymbol{x}}_2}} \right) $在10000个随机输入下的取值

    Fig. 1.  Values of convex discriminant function of $ F\left( {\theta , {{\boldsymbol{x}}_1}, {{\boldsymbol{x}}_2}} \right) $ with 10 thousand random input variables.

    图 2  密钥生成率随单个参数的变化曲线

    Fig. 2.  Curves of key rate versus each parameter of the input.

    图 3  LSA优化时不同初始点对密钥生成率的影响

    Fig. 3.  Influence of different start point on key rate using LSA optimization.

    图 4  利用不同优化算法所得密钥生成率对比

    Fig. 4.  Comparison among three key rates obtained by different optimization algorithm.

    目标函数$ {f_{{\text{LSA}}}}\left( {{x_1}, \cdots , {x_n}} \right) $
    根据经验初始化搜索位置$ {p_0} = \left( {x_1^0, \cdots , x_n^0} \right) $, 初始化迭代次数
    t = 0;
    while (迭代判决条件) do
     for k = 1∶n
      对$ {f_{{\text{LSA}}}}\left( {x_1^{t + 1}, \cdots , x_{k - 1}^{t + 1}, x_k^t, x_{k + 1}^t, \cdots , x_n^t} \right) $在$ x_k^t $维度上
      进行线性回溯搜索
      if ${f_{ {\text{LSA} } } }\left( {x_1^{t + 1}, \cdots , x_{k - 1}^{t + 1}, x_k^{t + 1}, x_{k + 1}^t, \cdots , x_n^t} \right) > $
        $ {f_{ {\text{LSA} } } }\left( {x_1^{t + 1}, \cdots , x_{k - 1}^{t + 1}, x_k^t, x_{k + 1}^t, \cdots , x_n^t} \right)$
       更新$ x_k^t $为$ x_k^{t + 1} $
       $ {p_{t + 1}} = \left( {x_1^{t + 1}, \cdots , x_{k - 1}^{t + 1}, x_k^{t + 1}, x_{k + 1}^t, \cdots , x_n^t} \right) $
      else
       $ {p_{t + 1}} = \left( {x_1^{t + 1}, \cdots , x_{k - 1}^{t + 1}, x_k^t, x_{k + 1}^t, \cdots , x_n^t} \right) $
      end
     end
     更新迭代次数 t = t + 1
     更新搜索位置为$ {p_{t + 1}} $
    end
    输出最终结果$ \left( {x_1^{t + 1}, \cdots , x_n^{t + 1}} \right) $和$ {f_{{\text{LSA}}}}\left( {x_1^{t + 1}, \cdots , x_n^{t + 1}} \right) $
    下载: 导出CSV
    目标函数$ f\left( {\boldsymbol{x}} \right) $
    根据经验初始化粒子1的位置$ {{\boldsymbol{x}}_1} $
    初始化剩余$ n - 1 $个粒子的位置$ {{\boldsymbol{x}}_i} $和所有粒子的速度$ {{\boldsymbol{\nu }}_i} $
    寻找全局最优解$ {{\boldsymbol{g}}_{\text{a}}} $, $ {{\boldsymbol{g}}_{\text{a}}} = \min \left\{ {f\left( {{{\boldsymbol{x}}_1}} \right), \cdots , f\left( {{{\boldsymbol{x}}_n}} \right)} \right\} $
    while(迭代判决条件) do
     for 所有的粒子 do
      更新速度$ {\boldsymbol{\nu }}_i^{t + 1} $
      更新位置$ {\boldsymbol{x}}_i^{t + 1} $
      计算目标函数在新位置的值
      更新当前粒子的历史最优位置$ {\boldsymbol{x}}_i^* $
     end
    更新全局最优解$ {{\boldsymbol{g}}_{\text{a}}} $
     end
    输出最终结果$ {\boldsymbol{x}}_i^* $和$ {{\boldsymbol{g}}_{\text{a}}} $
    以$ {{\boldsymbol{g}}_{\text{a}}} $为初始点, 采用LSA算法求局部最优解
    下载: 导出CSV

    表 1  用于仿真分析的相关参数

    Table 1.  Practical parameters for numerical simulations.

    ${\eta _{\text{d}}}$/%${e_{\text{d}}}$/%${Y_0}$${f_{\text{e}}}$$\chi $$N$$\alpha $
    14.51.5$6.02 \times {10^{ - 6}}$1.16${10^{ - 7}}$${10^{12}}$0.21
    下载: 导出CSV

    表 2  可判别密钥生成率非凸的四个点

    Table 2.  Four points which can be used to discriminate the key rate is non convex function.

    参数$ {{\boldsymbol{x}}_1} $$ {{\boldsymbol{x}}_2} $$ {{\boldsymbol{x}}_3} $$ {{\boldsymbol{x}}_4} $
    $ \mu $0.400.600.500.075
    $ \nu $0.0370.0450.029$5.9 \times {10^{ - 3} }$
    $ \omega $$7.9 \times {10^{ - 4} }$$2.6 \times {10^{ - 3} }$$2.0 \times {10^{ - 3} }$$2.57 \times {10^{ - 4} }$
    $ {P_\mu } $0.150.480.540.020
    $ {P_\nu } $0.180.130.260.48
    $ {P_{{\text{X}}|\mu }} $0.80.140.760.14
    $ {P_{{\text{X}}|\nu }} $0.920.560.890.64
    $ {P_{{\text{X}}|\omega }} $0.250.990.540.55
    $ \theta $0.470.64
    $ F\left( {\theta , {\boldsymbol{x}}, {\boldsymbol{y}}} \right) $$ - 5.50 \times {10^{ - 6}} $$ 3.84 \times {10^{ - 6}} $
    下载: 导出CSV

    表 3  三种优化算法计算资源消耗比较

    Table 3.  Comparison of computational resource consumption among the three optimization algorithms.

    算法迭代次数时间/s密钥生成率
    LSA8580.12$ 4.13 \times {10^{ - 6}} $
    PSO400004.2$ 2.97 \times {10^{ - 6}} $
    PSLSA405594.29$ 4.13 \times {10^{ - 6}} $
    下载: 导出CSV
  • [1]

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

    [2]

    Pirandola S, Andersen U L, Banchi L, Berta M, Bunandar D, Colbeck R, Englund D, Gehring T, Lupo C, Ottaviani C, Pereira J L, Razavi M, Shamsul Shaari J, Tomamichel M, Usenko V C, Vallone G, Villoresi P, Wallden P 2020 Adv. Opt. Photonics 12 1012Google Scholar

    [3]

    Ekert A K 1991 Phys. Rev. Lett. 67 661Google Scholar

    [4]

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

    [5]

    Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002Google Scholar

    [6]

    Gerhardt I, Liu Q, Lamas-Linares A, Skaar J, Kurtsiefer C, Makarov V 2011 Nat. Commun. 2 349Google Scholar

    [7]

    Jain N, Stiller B, Khan I, Elser D, Marquardt C, Leuchs G 2016 Contemp. Phys. 57 366Google Scholar

    [8]

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

    [9]

    Lo H K, Curty M, Qi B 2012 Phys. Rev. Lett. 108 130503Google Scholar

    [10]

    Gu J, Cao X Y, Fu Y, He Z W, Yin Z J, Yin H L, Chen Z B 2022 Sci. Bull. 67 2167Google Scholar

    [11]

    Yin H L, Cao W F, Fu Y, Tang Y L, Liu Y, Chen T Y, Chen Z B 2014 Opt. Lett. 39 5451Google Scholar

    [12]

    Lo H K, Chau H F, Ardehali M 2005 J. Cryptol. 18 133Google Scholar

    [13]

    Wei Z, Wang W, Zhang Z, Gao M, Ma Z, Ma X 2013 Sci. Rep. 3 2453Google Scholar

    [14]

    Xu F, Xu H, Lo H K 2014 Phys. Rev. A 89 052333Google Scholar

    [15]

    Wang W, Lo H K 2019 Phys. Rev. A 100 062334Google Scholar

    [16]

    Ding H J, Liu J Y, Zhang C M, Wang Q 2020 Quantum Inf. Process. 19 60Google Scholar

    [17]

    Dong Q, Huang G, Cui W, Jiao R 2022 Quantum Inf. Process. 21 233Google Scholar

    [18]

    Dong Q, Huang G, Cui W, Jiao R 2021 Quantum Sci. Technol. 7 015014

    [19]

    Lu F Y, Yin Z Q, Wang C, Cui C H, Teng J, Wang S, Chen W, Huang W, Xu B J, Guo G C, Han Z F 2019 J. Opt. Soc. Am. B 36 B92Google Scholar

    [20]

    Boyd S P, Vandenberghe L 2004 Convex Optimization (New York: Cambridge University Press) p716

    [21]

    韩宝玲, 赵锐, 罗庆生, 徐峰, 赵嘉珩 2017 北京理工大学学报 37 461

    Han B L, Zhao R, Luo Q S, Xu F, Zhao J H 2017 J. Beijing Inst. Technol. 37 461

    [22]

    蒋丽, 叶润舟, 梁昌勇, 陆文星 2019 计算机工程与应用 55 130

    Jiang L, Ye R Z, Liang C Y, Lu W X 2019 Computer Engineering and Applications 55 130

    [23]

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

    [24]

    Ma X, Zeng P, Zhou H 2018 Phys. Rev. X 8 031043

    [25]

    Zhou L, Lin J, Jing Y, Yuan Z 2023 Nat. Commun. 14 928Google Scholar

    [26]

    Zeng P, Zhou H, Wu W, Ma X 2022 Nat. Commun. 13 3903Google Scholar

    [27]

    Xie Y M, Lu Y S, Weng C X, Cao X Y, Jia Z Y, Bao Y, Wang Y, Fu Y, Yin H L, Chen Z B 2022 PRX Quantum. 3 020315Google Scholar

    [28]

    Ma X, Fung C H F, Razavi M 2012 Phys. Rev. A 86 052305Google Scholar

    [29]

    Sun S H, Gao M, Li C Y, Liang L M 2013 Phys. Rev. A 87 052329Google Scholar

    [30]

    Ma X, Qi B, Zhao Y, Lo H K 2005 Phys. Rev. A 72 012326Google Scholar

    [31]

    Curty M, Xu F, Cui W, Lim C C W, Tamaki K, Lo H K 2014 Nat. Commun. 5 3732Google Scholar

    [32]

    Xu F, Curty M, Qi B, Lo H K 2013 New J. Phys. 15 113007Google Scholar

    [33]

    Yang X S 2021 Nature-Inspired Optimization Algorithms (London: Elsevier) pp111–113

    [34]

    Gandomi A H, Yun G J, Yang X S, Talatahari S 2013 Commun. Nonlinear Sci. Numer. Simul. 18 327Google Scholar

    [35]

    Ursin R, Tiefenbacher F, Schmitt-Manderbach T, et al. 2007 Nat. Phys. 3 481Google Scholar

  • [1] 朱佳莉, 曹原, 张春辉, 王琴. 实用化量子密钥分发光网络中的资源优化配置. 物理学报, 2023, 72(2): 020301. doi: 10.7498/aps.72.20221661
    [2] 周阳, 马啸, 周星宇, 张春辉, 王琴. 实用化态制备误差容忍参考系无关量子密钥分发协议. 物理学报, 2023, 72(24): 240301. doi: 10.7498/aps.72.20231144
    [3] 刘天乐, 徐枭, 付博伟, 徐佳歆, 刘靖阳, 周星宇, 王琴. 基于回归决策树的测量设备无关型量子密钥分发参数优化. 物理学报, 2023, 72(11): 110304. doi: 10.7498/aps.72.20230160
    [4] 李鑫鹏, 曹睿杰, 李铭, 郭各朴, 李禹志, 马青玉. 基于粒子群算法的超振荡超分辨聚焦声场设计. 物理学报, 2022, 71(20): 204304. doi: 10.7498/aps.71.20220898
    [5] 陈以鹏, 刘靖阳, 朱佳莉, 方伟, 王琴. 机器学习在量子通信资源优化配置中的应用. 物理学报, 2022, 71(22): 220301. doi: 10.7498/aps.71.20220871
    [6] 马啸, 孙铭烁, 刘靖阳, 丁华建, 王琴. 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. 物理学报, 2022, 71(3): 030301. doi: 10.7498/aps.71.20211456
    [7] 李明飞, 袁梓豪, 刘院省, 邓意成, 王学锋. 光纤相控阵稀疏排布优化算法对比. 物理学报, 2021, 70(8): 084205. doi: 10.7498/aps.70.20201768
    [8] 杜聪, 王金东, 秦晓娟, 魏正军, 於亚飞, 张智明. 基于混合编码的测量设备无关量子密钥分发的简单协议. 物理学报, 2020, 69(19): 190301. doi: 10.7498/aps.69.20200162
    [9] 谷文苑, 赵尚弘, 东晨, 王星宇, 杨鼎. 参考系波动下的参考系无关测量设备无关量子密钥分发协议. 物理学报, 2019, 68(24): 240301. doi: 10.7498/aps.68.20191364
    [10] 吴承峰, 杜亚男, 王金东, 魏正军, 秦晓娟, 赵峰, 张智明. 弱相干光源测量设备无关量子密钥分发系统的性能优化分析. 物理学报, 2016, 65(10): 100302. doi: 10.7498/aps.65.100302
    [11] 杜亚男, 解文钟, 金璇, 王金东, 魏正军, 秦晓娟, 赵峰, 张智明. 基于弱相干光源测量设备无关量子密钥分发系统的误码率分析. 物理学报, 2015, 64(11): 110301. doi: 10.7498/aps.64.110301
    [12] 刘瑞兰, 王徐亮, 唐超. 基于粒子群算法的有机半导体NPB传输特性辨识. 物理学报, 2014, 63(2): 028105. doi: 10.7498/aps.63.028105
    [13] 陈颖, 王文跃, 于娜. 粒子群算法优化异质结构光子晶体环形腔滤波特性. 物理学报, 2014, 63(3): 034205. doi: 10.7498/aps.63.034205
    [14] 郑仕链, 杨小牛. 绿色认知无线电自适应参数调整. 物理学报, 2012, 61(14): 148402. doi: 10.7498/aps.61.148402
    [15] 王校锋, 薛红军, 司守奎, 姚跃亭. 基于粒子群算法和OGY方法的混沌系统混合控制. 物理学报, 2009, 58(6): 3729-3733. doi: 10.7498/aps.58.3729
    [16] 赵知劲, 徐世宇, 郑仕链, 杨小牛. 基于二进制粒子群算法的认知无线电决策引擎. 物理学报, 2009, 58(7): 5118-5125. doi: 10.7498/aps.58.5118
    [17] 张新陆, 王月珠, 李 立, 崔金辉, 鞠有伦. 端面抽运Tm,Ho∶YLF连续激光器的参数优化与实验研究. 物理学报, 2008, 57(6): 3519-3524. doi: 10.7498/aps.57.3519
    [18] 胡华鹏, 张 静, 王金东, 黄宇娴, 路轶群, 刘颂豪, 路 巍. 双协议量子密钥分发系统实验研究. 物理学报, 2008, 57(9): 5605-5611. doi: 10.7498/aps.57.5605
    [19] 陈 杰, 黎 遥, 吴 光, 曾和平. 偏振稳定控制下的量子密钥分发. 物理学报, 2007, 56(9): 5243-5247. doi: 10.7498/aps.56.5243
    [20] 陈 霞, 王发强, 路轶群, 赵 峰, 李明明, 米景隆, 梁瑞生, 刘颂豪. 运行双协议相位调制的量子密钥分发系统. 物理学报, 2007, 56(11): 6434-6440. doi: 10.7498/aps.56.6434
计量
  • 文章访问数:  2092
  • PDF下载量:  43
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-02-12
  • 修回日期:  2023-04-19
  • 上网日期:  2023-05-05
  • 刊出日期:  2023-06-20

/

返回文章
返回