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

基于极化-空间模超纠缠的量子网络多跳纠缠交换方法研究

杨光 刘琦 聂敏 刘原华 张美玲

引用本文:
Citation:

基于极化-空间模超纠缠的量子网络多跳纠缠交换方法研究

杨光, 刘琦, 聂敏, 刘原华, 张美玲

Multi-hop entanglement swapping in quantum networks based on polization-space hyperentanglement

Yang Guang, Liu Qi, Nie Min, Liu Yuan-Hua, Zhang Mei-Ling
PDF
HTML
导出引用
  • 基于纠缠交换方法进行多跳量子信息传输,是实现远距离量子网络通信的基本方式之一. 传统的多跳量子网络通常使用单自由度极化光子纠缠态作为量子信道, 信息传输容量较低且容易受到噪声的干扰. 本文提出一种基于超纠缠的高效量子网络多跳纠缠交换方法,利用极化-空间模式两自由度的纠缠光子, 建立超纠缠量子多跳信息传输通道. 以远程超纠缠隐形传态的信道建立需求为例, 首先给出了基础的逐跳超纠缠交换方案, 为降低该方案的端到端超纠缠建立时延, 提出在中间量子节点进行同时测量的并行超纠缠交换方案. 在此基础上, 为降低并行超纠缠交换的经典信息开销, 进一步提出一种分级并行超纠缠交换方案. 理论分析及仿真结果表明该方案的纠缠建立时延接近于并行超纠缠交换方案, 但可以减少经典信息传输量, 在一定程度上实现两者的平衡. 相比传统的纠缠交换方法, 本文方案有利于解决远程超纠缠通信的需求,对未来构建更高效率的量子网络有积极意义.
    Entanglement swapping (ES) based multi-hop quantum information transmission is a fundamental way to realize long-distance quantum communication. However, in the conventional quantum networks, the entanglement in one degree of freedom (DOF) of photon system is usually used as a quantum channel, showing disadvantages of low capacity and susceptibility to noise. In this paper, we present an efficient multi-hop quantum hyperentanglement swapping (HES) method based on hyperentanglement, which utilizes the entangled photos in polarization and spatial-mode DOFs to establish the hyperentangled multi-hop quantum channel. Taking long-distance hyperentanglement based quantum teleportation for example, we first describe a basic hop by hop HES scheme. Then, in order to reduce the end-to-end delay of this scheme, we propose a simultaneous HES (SHES) scheme, in which the intermediate quantum nodes perform hyperentangled Bell state measurements concurrently. On the basis of this scheme, we further put forward a hierarchical SHES (HSHES) scheme that can reduce the classical information cost. Theoretical analysis and simulation results show that the end-to-end delay of HSHES is similar to that of SHES, meanwhile, the classical information cost of HSHES is much lower than that of SHES, showing a better tradeoff between the two performance metrics. Compared with the traditional ES methods, the scheme proposed in this paper is conductive to meeting the requirements for long-distance hyperentanglement based quantum communication, which has positive significance for building more efficient quantum networks in the future.
      通信作者: 刘琦, valenti_67@foxmail.com
    • 基金项目: 国家自然科学基金(批准号: 61971348, 61201194)和陕西省自然科学基础研究计划(批准号: 2021JM-464 ) 资助的课题.
      Corresponding author: Liu Qi, valenti_67@foxmail.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61971348, 61201194) and the Natural Science Basic Research Program of Shaanxi Provence, China (Grant No. 2021JM-464).
    [1]

    Pan J W, Chen Z B, Lu Y C, Weinfurter H, Zeilinger A, Zukowsk M 2012 Rev. Mod. Phys. 84 777Google Scholar

    [2]

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

    [3]

    范桁 2018 物理学报 67 120301Google Scholar

    Fan H 2018 Acta Phys. Sin. 67 120301Google Scholar

    [4]

    Luo Y H, Zhong H S, Erhard M, Wang X L, Peng C L, Krenn M, Jiang X, Li L, Liu N L, Lu C Y, Zeilinger A, Pan J W 2019 Phys. Rev. Lett. 123 070505Google Scholar

    [5]

    Hassanpour S, Houshmand M 2016 Quantum Inf. Process 15 905Google Scholar

    [6]

    Zang P, Song R, Jiang Y 2017 Chinese Journal of Quantum Electronics 34 456

    [7]

    Paulson K G, Panigrahi P K 2019 Phys. Rev. A 100 052325Google Scholar

    [8]

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

    [9]

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

    [10]

    Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145Google Scholar

    [11]

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

    [12]

    曹正文, 赵光, 张爽浩, 冯晓毅, 彭进业 2016 物理学报 65 230301Google Scholar

    Cao Z W, Zhao G, Zhang S H, Feng X Y, Peng J Y 2016 Acta Phys. Sin. 65 230301Google Scholar

    [13]

    Chen J P, Zhang C, Liu Y, Jiang C, Zhang W J, Hu X L, Guan J Y, Yu Z W, Xu H, Lin J, Li M J, Chen H, Li H, You, L X, Wang Z, Wang X B, Zhang Q, Pan J W 2020 Phys. Rev. Lett. 124 070501Google Scholar

    [14]

    龙桂鲁, 潘栋 2021 信息通信技术与政策 7 7Google Scholar

    Long G L, Pan D 2021 Telecommunications Network Technology 7 7Google Scholar

    [15]

    Sheng Y B, Guo F G, Long G L 2010 Phys Rev. A 82 032318Google Scholar

    [16]

    Hong C H, Heo J, Lim J I, Yang H J 2014 Chin. Phys. B 23 090309Google Scholar

    [17]

    Wang X L, Cai X D, Su Z E, Cheng M C, Wu D, Li L, Liu N L, Lu C Y, Pan J W 2015 Nature 518 516Google Scholar

    [18]

    Xu L 2020 Modern Phys Lett. B 34 2050353Google Scholar

    [19]

    彭承志, 潘建伟 2016 中国科学院院刊 31 1096

    Peng C Z, Pan J W 2016 Bulletin of Chinese Academy of Sciences 31 1096

    [20]

    Liao S K, Cai W Q 2018 Phys. Rev. Lett. 120 030501Google Scholar

    [21]

    赖俊森, 赵文玉, 张海懿 2021 信息通信技术与政策 7 6Google Scholar

    Lai J S, Zhao W Y, Zhang H Y 2021 Telecommunications Network Technology 7 6Google Scholar

    [22]

    聂敏, 张帆, 杨光, 张美玲, 孙爱晶, 裴昌幸 2021 物理学报 70 040303Google Scholar

    Nie M, Zhang F, Yang G, Zhang M L, Sun A J, Pei C X 2021 Acta Phys. Sin. 70 040303Google Scholar

    [23]

    杨光, 廉保旺, 聂敏 2015 物理学报 64 010303Google Scholar

    Yang G, Lian B W, Nie M 2015 Acta Phys. Sin. 64 010303Google Scholar

    [24]

    杨光, 廉保旺, 聂敏 2015 物理学报 64 240304Google Scholar

    Yang G, Lian B W, Nie M 2015 Acta Phys. Sin. 64 240304Google Scholar

    [25]

    Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910Google Scholar

    [26]

    Pan J W, Bouwmeester D, Weinfurter H, Zeilinger A 1998 Phys. Rev. Lett. 80 3891Google Scholar

    [27]

    Dotsenko I S, Korobka R 2018 Commun. Theor. Phys. 69 143Google Scholar

    [28]

    Li Y H, Li X L, Nie L P, Sang M H 2016 Int. J. Theor. Phys. 55 1820Google Scholar

    [29]

    Tao Y X, Xu J, Zhang Z C 2013 Chin. Phys. B 22 090311Google Scholar

    [30]

    Espoukeh P, Pedram P 2014 Int. J. Theor. Phys. 13 1789

    [31]

    Du Z L, Li X L, Liu X J 2020 Int. J. Theor. Phys. 59 622Google Scholar

    [32]

    Gao X Q, Zhang Z C, Gong Y X, Sheng B, Yu X T 2017 J. Opt. Soc. Am. B-Opt. Phys. 34 142Google Scholar

    [33]

    Cai X F, Yu X T, Shi L H, Zhang Z C 2014 Front. Phys. 9 646Google Scholar

    [34]

    Xiong P Y, Yu X T, Zhang Z C, Zhan H T, Hua J Y 2017 Front. Phys. 12 1

    [35]

    Wang K, Yu X T, Lu S L, Gong X Y 2014 Phys Rev. A 89 022329Google Scholar

    [36]

    Tao Y, Zhang Q, Zhang J, Yin J, Zhao Z, Zukowski M, Chen Z B, Pan J W 2005 Phys. Rev. Lett. 95 240406Google Scholar

    [37]

    郭肖 2020 硕士学位论文 (西安: 西安电子科技大学 )

    Guo X 2020 M. S. Dissertation (Shannxi: Xidian University) (in Chinese)

    [38]

    聂敏, 王超旭, 杨光, 张美玲, 孙爱晶, 裴昌幸 2021 物理学报 70 030301Google Scholar

    Nie M, Wang C X, Yang G, Sun A J, Pei C X 2021 Acta Phys. Sin. 70 030301Google Scholar

    [39]

    张秀再, 徐茜, 刘邦宇 2020 光学学报 40 0327001Google Scholar

    Zhang X Z, Xu Q, Liu B Y 2020 Acta Optica Sinica 40 0327001Google Scholar

    [40]

    Xu J, Chen X G, Xiao H W, Wang P X, Ma M 2021 Appl. Sci. 11 10869Google Scholar

    [41]

    Cabello A 2000 Phys. Rev. Lett. 85 5635Google Scholar

  • 图 1  极化和空间模自由度中超纠缠态产生原理

    Fig. 1.  Schematic diagram of the setup to generate hyperentanglement in both polarization and spatial-mode DOFs.

    图 2  超纠缠交换原理

    Fig. 2.  Schematic diagram of hyperentanglement swapping.

    图 3  并行超纠缠交换

    Fig. 3.  Schematic diagram of simultaneous hyperentanglement swapping.

    图 4  多级并行纠缠交换原理

    Fig. 4.  Schematic diagram of hierarchical simultaneous entanglement swapping.

    图 5  隐形传态保真度

    Fig. 5.  Teleportation fidelity.

    图 6  隐形传态保真度随跳数及幅值阻尼系数的变化

    Fig. 6.  Teleportation fidelity versus the number of hops and the damping factor.

    图 7  端到端纠缠建立时延随中间节点个数的关系

    Fig. 7.  Time delay versus the number of intermediate nodes.

    图 8  单跳距离与端到端时延的关系

    Fig. 8.  End to end time delay versus the per-hop length.

    图 9  跳数选择与隐形传态保真度的关系

    Fig. 9.  Teleportation fidelity versus the choice of the number of hops.

    图 10  中间节点数与经典信息开销关系

    Fig. 10.  Classical costs versus the number of intermediate nodes.

    图 11  每段节点数与经典信息开销的关系

    Fig. 11.  Classical costs versus number of intermediate nodes in one segment.

    图 12  跳数与纠缠交换效率的关系

    Fig. 12.  Entanglement swapping efficiency versus the number of hops.

    表 1  幺正变换表

    Table 1.  Unitary operations.

    B和C的量子态编码结果AD的量子态Bob的幺正变换
    $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^{\text{ + }}}} \right\rangle _{S} $0000$ \left| {{\phi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^{\text{ + }}}} \right\rangle _{S} $$ {U_1} = \sigma _I^P \otimes \sigma _I^S $
    $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $0001$ \left| {{\phi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $$ {U_2} = \sigma _I^P \otimes \sigma _Z^S $
    $ \left| {{\phi ^ - }} \right\rangle _{P} \left| {{\phi ^ + }} \right\rangle _{S} $0010$ \left| {{\phi ^ - }} \right\rangle _{P} \left| {{\phi ^ + }} \right\rangle _{S} $$ {U_3} = \sigma _Z^P \otimes \sigma _I^S $
    $ \left| {{\phi ^ - }} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $0011$ \left| {{\phi ^ - }} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $$ {U_4} = \sigma _Z^P \otimes \sigma _Z^S $
    $ \left| {{\psi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^{\text{ + }}}} \right\rangle _{S} $0100$ \left| {{\psi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^{\text{ + }}}} \right\rangle _{S} $$ {U_5} = \sigma _X^P \otimes \sigma _I^S $
    $ \left| {{\psi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $0101$ \left| {{\psi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $$ {U_6} = \sigma _X^P \otimes \sigma _Z^S $
    $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\phi ^ + }} \right\rangle _{S} $0110$ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\phi ^ + }} \right\rangle _{S} $${U_7} = - {{i}}\sigma _Y^P \otimes \sigma _I^S$
    $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $0111$ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $${U_8} = - {{i}}\sigma _Y^P \otimes \sigma _Z^S$
    $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{p} \left| {{\psi ^{\text{ + }}}} \right\rangle _{S} $1000$ \left| {{\phi ^{\text{ + }}}} \right\rangle _{p} \left| {{\psi ^{\text{ + }}}} \right\rangle _{S} $$ {U_9} = \sigma _I^P \otimes \sigma _X^S $
    $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{p} \left| {{\psi ^ - }} \right\rangle _{S} $1001$ \left| {{\phi ^{\text{ + }}}} \right\rangle _{p} \left| {{\psi ^ - }} \right\rangle _{S} $${U_{10} } = \sigma _I^P \otimes - {{i}}\sigma _Y^S$
    $ \left| {{\phi ^ - }} \right\rangle _{p} \left| {{\psi ^ + }} \right\rangle _{S} $1010$ \left| {{\phi ^ - }} \right\rangle _{p} \left| {{\psi ^ + }} \right\rangle _{S} $$ {U_{11}} = \sigma _Z^P \otimes \sigma _X^S $
    $ \left| {{\phi ^ - }} \right\rangle _{p} \left| {{\psi ^ - }} \right\rangle _{S} $1011$ \left| {{\phi ^ - }} \right\rangle _{p} \left| {{\psi ^ - }} \right\rangle _{S} $${U_{12} } = \sigma _Z^P \otimes - {{i}}\sigma _Y^S$
    $ \left| {{\psi ^ + }} \right\rangle _{P} \left| {{\psi ^ + }} \right\rangle _{S} $1100$ \left| {{\psi ^ + }} \right\rangle _{P} \left| {{\psi ^ + }} \right\rangle _{S} $$ {U_{13}} = \sigma _X^P \otimes \sigma _X^S $
    $ \left| {{\psi ^ + }} \right\rangle _{P} \left| {{\psi ^ - }} \right\rangle _{S} $1101$ \left| {{\psi ^ + }} \right\rangle _{P} \left| {{\psi ^ - }} \right\rangle _{S} $${U_{14} } = \sigma _X^P \otimes - {{i}}\sigma _Y^S$
    $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\psi ^ + }} \right\rangle _{S} $1110$ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\psi ^ + }} \right\rangle _{S} $${U_{15} } = - {{i}}\sigma _Y^P \otimes \sigma _X^S$
    $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\psi ^ - }} \right\rangle _{S} $1111$ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\psi ^ - }} \right\rangle _{S} $${U_{16} } = - {{i}}\sigma _Y^P \otimes - {\rm{i} }\sigma _Y^S$
    下载: 导出CSV

    表 2  多跳并行幺正变换表

    Table 2.  Multi-hop parallel entanglement swapping unitary operations

    N1, N2, ···NN – 1 测量结果Alice的幺正变换
    $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $$ {U_1} = \sigma _I^P \otimes \sigma _I^S $
    $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $$ {U_2} = \sigma _I^P \otimes \sigma _Z^S $
    $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $$ {U_3} = \sigma _I^P \otimes \sigma _X^S $
    $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $$ {U_4} = \sigma _I^P \otimes - i\sigma _Y^S $
    $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $$ {U_5} = \sigma _I^P \otimes \sigma _I^S $
    $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $$ {U_6} = \sigma _Z^P \otimes \sigma _Z^S $
    $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $$ {U_7} = \sigma _Z^P \otimes \sigma _X^S $
    $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $$ {U_8} = \sigma _Z^P \otimes - i\sigma _Y^S $
    $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $$ {U_9} = \sigma _X^P \otimes \sigma _I^S $
    $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $$ {U_{10}} = \sigma _X^P \otimes \sigma _Z^S $
    $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $$ {U_{11}} = \sigma _X^P \otimes \sigma _X^S $
    $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $$ {U_{12}} = \sigma _X^P \otimes - i\sigma _Y^S $
    $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $$ {U_{13}} = - i\sigma _Y^P \otimes \sigma _I^S $
    $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $$ {U_{14}} = - i\sigma _Y^P \otimes \sigma _Z^S $
    $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $$ {U_{15}} = - i\sigma _Y^P \otimes \sigma _X^S $
    $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $$ {U_{1{\text{6}}}} = - i\sigma _Y^P \otimes - i\sigma _Y^S $
    下载: 导出CSV
  • [1]

    Pan J W, Chen Z B, Lu Y C, Weinfurter H, Zeilinger A, Zukowsk M 2012 Rev. Mod. Phys. 84 777Google Scholar

    [2]

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

    [3]

    范桁 2018 物理学报 67 120301Google Scholar

    Fan H 2018 Acta Phys. Sin. 67 120301Google Scholar

    [4]

    Luo Y H, Zhong H S, Erhard M, Wang X L, Peng C L, Krenn M, Jiang X, Li L, Liu N L, Lu C Y, Zeilinger A, Pan J W 2019 Phys. Rev. Lett. 123 070505Google Scholar

    [5]

    Hassanpour S, Houshmand M 2016 Quantum Inf. Process 15 905Google Scholar

    [6]

    Zang P, Song R, Jiang Y 2017 Chinese Journal of Quantum Electronics 34 456

    [7]

    Paulson K G, Panigrahi P K 2019 Phys. Rev. A 100 052325Google Scholar

    [8]

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

    [9]

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

    [10]

    Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145Google Scholar

    [11]

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

    [12]

    曹正文, 赵光, 张爽浩, 冯晓毅, 彭进业 2016 物理学报 65 230301Google Scholar

    Cao Z W, Zhao G, Zhang S H, Feng X Y, Peng J Y 2016 Acta Phys. Sin. 65 230301Google Scholar

    [13]

    Chen J P, Zhang C, Liu Y, Jiang C, Zhang W J, Hu X L, Guan J Y, Yu Z W, Xu H, Lin J, Li M J, Chen H, Li H, You, L X, Wang Z, Wang X B, Zhang Q, Pan J W 2020 Phys. Rev. Lett. 124 070501Google Scholar

    [14]

    龙桂鲁, 潘栋 2021 信息通信技术与政策 7 7Google Scholar

    Long G L, Pan D 2021 Telecommunications Network Technology 7 7Google Scholar

    [15]

    Sheng Y B, Guo F G, Long G L 2010 Phys Rev. A 82 032318Google Scholar

    [16]

    Hong C H, Heo J, Lim J I, Yang H J 2014 Chin. Phys. B 23 090309Google Scholar

    [17]

    Wang X L, Cai X D, Su Z E, Cheng M C, Wu D, Li L, Liu N L, Lu C Y, Pan J W 2015 Nature 518 516Google Scholar

    [18]

    Xu L 2020 Modern Phys Lett. B 34 2050353Google Scholar

    [19]

    彭承志, 潘建伟 2016 中国科学院院刊 31 1096

    Peng C Z, Pan J W 2016 Bulletin of Chinese Academy of Sciences 31 1096

    [20]

    Liao S K, Cai W Q 2018 Phys. Rev. Lett. 120 030501Google Scholar

    [21]

    赖俊森, 赵文玉, 张海懿 2021 信息通信技术与政策 7 6Google Scholar

    Lai J S, Zhao W Y, Zhang H Y 2021 Telecommunications Network Technology 7 6Google Scholar

    [22]

    聂敏, 张帆, 杨光, 张美玲, 孙爱晶, 裴昌幸 2021 物理学报 70 040303Google Scholar

    Nie M, Zhang F, Yang G, Zhang M L, Sun A J, Pei C X 2021 Acta Phys. Sin. 70 040303Google Scholar

    [23]

    杨光, 廉保旺, 聂敏 2015 物理学报 64 010303Google Scholar

    Yang G, Lian B W, Nie M 2015 Acta Phys. Sin. 64 010303Google Scholar

    [24]

    杨光, 廉保旺, 聂敏 2015 物理学报 64 240304Google Scholar

    Yang G, Lian B W, Nie M 2015 Acta Phys. Sin. 64 240304Google Scholar

    [25]

    Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910Google Scholar

    [26]

    Pan J W, Bouwmeester D, Weinfurter H, Zeilinger A 1998 Phys. Rev. Lett. 80 3891Google Scholar

    [27]

    Dotsenko I S, Korobka R 2018 Commun. Theor. Phys. 69 143Google Scholar

    [28]

    Li Y H, Li X L, Nie L P, Sang M H 2016 Int. J. Theor. Phys. 55 1820Google Scholar

    [29]

    Tao Y X, Xu J, Zhang Z C 2013 Chin. Phys. B 22 090311Google Scholar

    [30]

    Espoukeh P, Pedram P 2014 Int. J. Theor. Phys. 13 1789

    [31]

    Du Z L, Li X L, Liu X J 2020 Int. J. Theor. Phys. 59 622Google Scholar

    [32]

    Gao X Q, Zhang Z C, Gong Y X, Sheng B, Yu X T 2017 J. Opt. Soc. Am. B-Opt. Phys. 34 142Google Scholar

    [33]

    Cai X F, Yu X T, Shi L H, Zhang Z C 2014 Front. Phys. 9 646Google Scholar

    [34]

    Xiong P Y, Yu X T, Zhang Z C, Zhan H T, Hua J Y 2017 Front. Phys. 12 1

    [35]

    Wang K, Yu X T, Lu S L, Gong X Y 2014 Phys Rev. A 89 022329Google Scholar

    [36]

    Tao Y, Zhang Q, Zhang J, Yin J, Zhao Z, Zukowski M, Chen Z B, Pan J W 2005 Phys. Rev. Lett. 95 240406Google Scholar

    [37]

    郭肖 2020 硕士学位论文 (西安: 西安电子科技大学 )

    Guo X 2020 M. S. Dissertation (Shannxi: Xidian University) (in Chinese)

    [38]

    聂敏, 王超旭, 杨光, 张美玲, 孙爱晶, 裴昌幸 2021 物理学报 70 030301Google Scholar

    Nie M, Wang C X, Yang G, Sun A J, Pei C X 2021 Acta Phys. Sin. 70 030301Google Scholar

    [39]

    张秀再, 徐茜, 刘邦宇 2020 光学学报 40 0327001Google Scholar

    Zhang X Z, Xu Q, Liu B Y 2020 Acta Optica Sinica 40 0327001Google Scholar

    [40]

    Xu J, Chen X G, Xiao H W, Wang P X, Ma M 2021 Appl. Sci. 11 10869Google Scholar

    [41]

    Cabello A 2000 Phys. Rev. Lett. 85 5635Google Scholar

  • [1] 刘然, 吴泽, 李宇晨, 陈昱全, 彭新华. 基于量子Fisher信息测量的实验多体纠缠刻画. 物理学报, 2023, 72(11): 110305. doi: 10.7498/aps.72.20230356
    [2] 卫容宇, 李军, 张大命, 王炜皓. 纠缠态量子探测系统的恒虚警检测方法研究. 物理学报, 2022, 71(1): 010303. doi: 10.7498/aps.71.20211121
    [3] 卫容宇, 李军, 张大命, 王炜皓. 纠缠态量子探测系统的恒虚警检测方法研究. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211121
    [4] 李娟, 李佳明, 蔡春晓, 孙恒信, 刘奎, 郜江瑞. 优化抽运空间分布实现连续变量超纠缠的纠缠增强. 物理学报, 2019, 68(3): 034204. doi: 10.7498/aps.68.20181625
    [5] 聂敏, 卫容宇, 杨光, 张美玲, 孙爱晶, 裴昌幸. 基于袋鼠纠缠跳跃模型的量子状态自适应跳变通信策略. 物理学报, 2019, 68(11): 110301. doi: 10.7498/aps.68.20190163
    [6] 朱浩男, 吴德伟, 李响, 王湘林, 苗强, 方冠. 基于纠缠见证的路径纠缠微波检测方法. 物理学报, 2018, 67(4): 040301. doi: 10.7498/aps.67.20172164
    [7] 宗晓岚, 杨名. 多粒子纠缠的保护方案. 物理学报, 2016, 65(8): 080303. doi: 10.7498/aps.65.080303
    [8] 陈鹏, 蔡有勋, 蔡晓菲, 施丽慧, 余旭涛. 基于纠缠态的量子通信网络的量子信道建立速率模型. 物理学报, 2015, 64(4): 040301. doi: 10.7498/aps.64.040301
    [9] 丁东, 何英秋, 闫凤利, 高亭. 六光子超纠缠态制备方案. 物理学报, 2015, 64(16): 160301. doi: 10.7498/aps.64.160301
    [10] 任宝藏, 邓富国. 光子两自由度超并行量子计算与超纠缠态操控. 物理学报, 2015, 64(16): 160303. doi: 10.7498/aps.64.160303
    [11] 杨光, 廉保旺, 聂敏. 多跳噪声量子纠缠信道特性及最佳中继协议. 物理学报, 2015, 64(24): 240304. doi: 10.7498/aps.64.240304
    [12] 赵建辉, 王海涛. 应用多尺度纠缠重整化算法研究量子自旋系统的量子相变和基态纠缠. 物理学报, 2012, 61(21): 210502. doi: 10.7498/aps.61.210502
    [13] 胡要花. 运动原子多光子J-C模型中的熵交换与纠缠. 物理学报, 2012, 61(12): 120302. doi: 10.7498/aps.61.120302
    [14] 李伟, 范明钰, 王光卫. 基于纠缠交换的仲裁量子签名方案. 物理学报, 2011, 60(8): 080302. doi: 10.7498/aps.60.080302
    [15] 王海霞, 殷雯, 王芳卫. 耦合量子点中的纠缠测量. 物理学报, 2010, 59(8): 5241-5245. doi: 10.7498/aps.59.5241
    [16] 唐有良, 刘 翔, 张小伟, 唐筱芳. 用一个纠缠态实现多粒子纠缠态的量子隐形传送. 物理学报, 2008, 57(12): 7447-7451. doi: 10.7498/aps.57.7447
    [17] 王菊霞, 杨志勇, 安毓英. 多模光场与二能级原子相互作用的纠缠交换与保持. 物理学报, 2007, 56(11): 6420-6426. doi: 10.7498/aps.56.6420
    [18] 冯发勇, 张 强. 基于超纠缠交换的量子密钥分发. 物理学报, 2007, 56(4): 1924-1927. doi: 10.7498/aps.56.1924
    [19] 杨宇光, 温巧燕, 朱甫臣. 基于纠缠交换的多方多级量子密钥分配协议. 物理学报, 2005, 54(12): 5544-5548. doi: 10.7498/aps.54.5544
    [20] 石名俊, 杜江峰, 朱栋培. 量子纯态的纠缠度. 物理学报, 2000, 49(5): 825-829. doi: 10.7498/aps.49.825
计量
  • 文章访问数:  2329
  • PDF下载量:  47
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-11-25
  • 修回日期:  2022-01-11
  • 上网日期:  2022-02-21
  • 刊出日期:  2022-05-20

/

返回文章
返回