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

非马尔科夫环境中Werner态的量子非局域关联检验研究

蒋世民 贾欣燕 樊代和

引用本文:
Citation:

非马尔科夫环境中Werner态的量子非局域关联检验研究

蒋世民, 贾欣燕, 樊代和

Quantum non-local correlation testing of Werner state in non-Markovian environment

Jiang Shi-Min, Jia Xin-Yan, Fan Dai-He
PDF
HTML
导出引用
  • 以量子信息领域中常使用的Werner态为研究对象, 详细地研究了其在两种非马尔科夫相位阻尼环境, 即Random-Telegraph (RT)噪声环境、Ornstein-Uhlenbeck (OU)噪声环境, 以及非马尔科夫振幅阻尼(AD)环境中演化后的量子非局域关联检验情况. 分别推导了Werner态在RT, OU以及AD环境中密度矩阵随时间的演化结果. 基于Clauser-Horne-Shimony-Holt (CHSH)不等式, 对演化后的量子态进行了详细的量子非局域关联检验研究. 结果表明, Werner态在RT噪声环境和AD环境中存在信息回流现象, 导致其量子非局域关联特性存在周期性振荡变化的现象, 即随演化时间的增加, 量子态能够从不具备量子非局域关联特性重新回到具有量子非局域关联特性的情况. 而在OU噪声环境中, 由于不存在信息回流现象, 量子非局域关联检验值将随演化时间的增加而降低. 同时, 本文还详细给出了Werner的保真度、量子态与非马尔科夫环境的耦合强度、OU噪声环境和AD环境的线宽、RT环境噪声的翻转率等参数与成功进行量子非局域关联检验的演化时间之间的关系.
    Research on whether quantum states retain quantum non-local correlation properties after evolving in non-Markovian environments has significant applications in the field of quantum information. In this work, we investigate the density matrix of quantum states evolving with time in various non-Markovian environments. Specifically, we examine two types of non-Markovian phase damping environments, namely random telegraph (RT) noise environment and Ornstein-Uhlenbeck (OU) noise environment, and non-Markovian amplitude damping (AD) environment. By utilizing the Clauser-Horne-Shimony-Holt (CHSH) inequality, a quantum non-local correlation testing of the Werner state after its evolution in these non-Markovian environments is conducted. The results show significant differences in the quantum non-local correlation testing results of the Werner state after evolving in different non-Markovian environments. Notably, the Werner state displays information backflow in the RT noise environment and the AD environment, resulting in periodic oscillations in its quantum non-local correlation testing. This suggests that under certain conditions, the quantum state can transition from a state without quantum non-local correlation back to a state with such a correlation as evolution time progresses. The results also show that the Werner state exhibits the information about backflow phenomena in RT noise environment and AD environment, leading to periodic oscillations in its quantum non-local correlation testing. Furthermore, these periods are inversely proportional to certain parameters, such as $\sqrt {{{\left( {{{2\gamma } \mathord{\left/ {\vphantom {{2\gamma } a}} \right. } a}} \right)}^2} - 1} $ and $ \sqrt {2{\varGamma \mathord{\left/ {\vphantom {\varGamma \gamma }} \right. } \gamma } - {{\left( {{\varGamma \mathord{\left/ {\vphantom {\varGamma \gamma }} \right. } \gamma }} \right)}^2}} $. On the contrary, in the OU noise environment, no information about backflow is obtained, thereby leading the value of the quantum non-local correlation test to increase with evolution time increasing. In most of AD and OU noise environments, there exists a specific maximum evolution time $\gamma {t_{\max }}$ in which successful quantum non-local correlation testing can be conducted. This maximum evolution time $\gamma {t_{\max }}$ shows a nonlinear variation with fidelity increasing and an inverse variation with $\varGamma /\gamma $ parameter increasing. In comparison, the maximum evolution time for successful quantum non-local correlation testing in the OU noise environment exceeds that in the AD environment under the same conditions, indicating that the AD environment exerts a more pronounced weakening effect on the quantum non-local correlation properties of the Werner state.
      通信作者: 樊代和, dhfan@swjtu.edu.cn
    • 基金项目: 国家自然科学基金 (批准号: 62374139)和计算物理国防科技重点实验室项目(批准号: 6142A05180401)资助的课题.
      Corresponding author: Fan Dai-He, dhfan@swjtu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 62374139) and the Key Laboratory Project of Computational Physics of National Defense Science and Technology of China (Grant No. 6142A05180401).
    [1]

    Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. Lett. 47 777Google Scholar

    [2]

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

    [3]

    Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881Google Scholar

    [4]

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

    [5]

    Bell J S 1964 Physics 1 195Google Scholar

    [6]

    Clauser J F, Horne M A, Shimony A, Holt R A 1969 Phys. Rev. Lett. 23 880Google Scholar

    [7]

    Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865Google Scholar

    [8]

    Collins D, Gisin N 2004 J. Phys. A: Math. Gen. 37 1775Google Scholar

    [9]

    Greenberger D M, Horne M A, Shimony A, Zeilinger A 1990 Am. J. Phys. 58 1131Google Scholar

    [10]

    Hardy L 1993 Phys. Rev. Lett. 71 1665Google Scholar

    [11]

    胡强, 曾柏云, 辜鹏宇, 贾欣燕, 樊代和 2022 物理学报 71 070301Google Scholar

    Hu Q, Zeng B Y, Gu P Y, Jia X Y, Fan D H 2022 Acta Phys. Sin. 71 070301Google Scholar

    [12]

    曾柏云, 辜鹏宇, 蒋世民, 贾欣燕, 樊代和 2023 物理学报 72 050301Google Scholar

    Zeng B Y, Gu P Y, Jiang S M, Jia X Y, Fan D H 2023 Acta Phys. Sin. 72 050301Google Scholar

    [13]

    Rivas Á, Huelga S F, Plenio M B 2014 Rep. Prog. Phys. 77 094001Google Scholar

    [14]

    Breuer H P, Laine E M, Piilo J, Vacchini B 2016 Rev. Mod. Phys. 88 021002Google Scholar

    [15]

    de Vicente J I, Spee C, Sauerwein D, Kraus B 2017 Phys. Rev. A 95 012323Google Scholar

    [16]

    Li L, Hall M J W, Wiseman H M 2018 Phys. Rep. 759 1Google Scholar

    [17]

    Weissman M B 1988 Rev. Mod. Phys. 60 537Google Scholar

    [18]

    Mi X, Cady J V, Zajac D M, Deelman P W, Petta J R 2017 Science 355 156Google Scholar

    [19]

    Groeblacher S, Trubarov A, Prigge N, Cole G D, Aspelmeyer M, Eisert J 2015 Nat. Commun. 6 7606Google Scholar

    [20]

    Potočnik A, Bargerbos A, Schröder F A Y N, Khan S A, Collodo M C, Gasparinetti S, Salathé Y, Creatore C, Eichler C, Türeci H E, Chin A W, Wallraff A 2018 Nat. Commun. 9 904Google Scholar

    [21]

    Haikka P, McEndoo S, De Chiara G, Palma G M, Maniscalco S 2011 Phys. Rev. A 84 031602Google Scholar

    [22]

    Utagi S, Srikanth R, Banerjee S 2020 Sci. Rep. 10 15049Google Scholar

    [23]

    Naikoo J, Banerjee S, Chandrashekar C M 2020 Phys. Rev. A 102 062209Google Scholar

    [24]

    Yu T, Eberly J 2007 Quantum Inf. Comput. 7 459Google Scholar

    [25]

    Kraus K 1971 Ann. Phys. 64 311Google Scholar

    [26]

    Rivas Á, Huelga S F, Plenio M B 2010 Phys. Rev. Lett. 105 050403Google Scholar

    [27]

    Breuer H P, Laine E M, Piilo J 2009 Phys. Rev. Lett. 103 210401Google Scholar

    [28]

    Pinto J P, Karpat G, Fanchini F F 2013 Phys. Rev. A. 88 034304Google Scholar

    [29]

    Yu T, Eberly J 2010 Opt. Commun. 283 676Google Scholar

    [30]

    Bellomo B, Franco R L, Compagno G 2007 Phys. Rev. Lett. 99 160502Google Scholar

    [31]

    Horodecki R, Horodecki P, Horodecki M 1995 Phys. Lett. A 200 340Google Scholar

  • 图 1  Werner态在RT噪声境中的量子非局域关联检验情况 (a) 当保真度$ F = 1 $时, 不同参数$\gamma /a$下$S_{}^{{\text{RT}}}$随$at$的变化曲线; (b) 当固定环境参数为$\gamma /a = 40$时, 不同F下的$S_{}^{{\text{RT}}}$随$at$的变化曲线

    Fig. 1.  Quantum non-local correlation testing of Werner state in RT noise environment: (a) $S_{}^{{\text{RT}}}$ versus evolution time $at$ under different $\gamma /a$ when $ F = 1 $; (b) $S_{}^{{\text{RT}}}$ versus evolution time $at$ under different fidelities when $\gamma /a = 40$

    图 2  RT噪声环境中${F_{\min }}$随$\gamma /a$的变换关系曲线

    Fig. 2.  ${F_{\min }}$ versus $\gamma /a$ in RT noise environment.

    图 3  Werner态在OU噪声境中的量子非局域关联检验情况 (a) 当保真度$ F = 1 $时, 不同环境参数$\varGamma /\gamma $下的$ S_{}^{{\text{OU}}} $随$\gamma t$的变化曲线; (b) 当固定$\varGamma /\gamma = 0.01$时, 不同F参数下的$ S_{}^{{\text{OU}}} $随$\gamma t$的变化曲线

    Fig. 3.  Quantum non-local correlation testing of Werner state in OU noise environment: (a) $ S_{}^{{\text{OU}}} $ versus evolution time $\gamma t$ under different $\varGamma /\gamma $ when $ F = 1 $; (b) $S_{}^{{\text{OU}}}$ versus evolution time $\gamma t$ under different fidelities when $\varGamma /\gamma = 0.01$.

    图 4  OU噪声环境中$\gamma {t_{\max }}$随$\varGamma /\gamma $, F的变化关系曲线(a)不同F下, $\gamma {t_{\max }}$随$\varGamma /\gamma $的变化曲线; (b) 不同$\varGamma /\gamma $下, $\gamma {t_{\max }}$随F的变化曲线

    Fig. 4.  $\gamma {t_{\max }}$ versus $\varGamma /\gamma $ and F respectively in OU noise environment: (a) $\gamma {t_{\max }}$ versus $\varGamma /\gamma $ under different F; (b) $\gamma {t_{\max }}$ versus F under different $\varGamma /\gamma $.

    图 5  Werner态在振幅阻尼环境中的量子非局域关联检验情况 (a) 当保真度$ F = 1 $时, 不同$\varGamma /\gamma $参数下的$S_{}^{{\text{AD}}}$随演化时间$\gamma t$的变化曲线; (b) 当$\varGamma /\gamma = 0.0020$时, 不同F下的$S_{}^{{\text{AD}}}$随演化时间$\gamma t$的变化曲线

    Fig. 5.  Quantum non-local correlation testing of Werner state in amplitude damping environment: (a) $S_{}^{{\text{AD}}}$ versus evolution time $\gamma t$ under different $\varGamma /\gamma $ when $ F = 1 $; (b) $S_{}^{{\text{AD}}}$ versus evolution time $\gamma t$ under different fidelities when $\varGamma /\gamma = 0.0020$.

    图 6  振幅阻尼环境中${F_{\min }}$随$\varGamma /\gamma $的变化关系曲线

    Fig. 6.  ${F_{\min }}$ versus $\varGamma /\gamma $ in amplitude damping environment.

    图 7  振幅阻尼环境中$\gamma {t_{\max }}$随$\varGamma /\gamma $, F的变化关系曲线(a) 不同F下, $\gamma {t_{\max }}$随$\varGamma /\gamma $的变化曲线; (b) 不同$\varGamma /\gamma $下, $\gamma {t_{\max }}$随F的变化曲线

    Fig. 7.  $\gamma {t_{\max }}$ versus $\varGamma /\gamma $ and F respectively in amplitude damping environment: (a) $\gamma {t_{\max }}$ versus $\varGamma /\gamma $ under different F; (b) $\gamma {t_{\max }}$ versus F under different $\varGamma /\gamma $.

  • [1]

    Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. Lett. 47 777Google Scholar

    [2]

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

    [3]

    Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881Google Scholar

    [4]

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

    [5]

    Bell J S 1964 Physics 1 195Google Scholar

    [6]

    Clauser J F, Horne M A, Shimony A, Holt R A 1969 Phys. Rev. Lett. 23 880Google Scholar

    [7]

    Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865Google Scholar

    [8]

    Collins D, Gisin N 2004 J. Phys. A: Math. Gen. 37 1775Google Scholar

    [9]

    Greenberger D M, Horne M A, Shimony A, Zeilinger A 1990 Am. J. Phys. 58 1131Google Scholar

    [10]

    Hardy L 1993 Phys. Rev. Lett. 71 1665Google Scholar

    [11]

    胡强, 曾柏云, 辜鹏宇, 贾欣燕, 樊代和 2022 物理学报 71 070301Google Scholar

    Hu Q, Zeng B Y, Gu P Y, Jia X Y, Fan D H 2022 Acta Phys. Sin. 71 070301Google Scholar

    [12]

    曾柏云, 辜鹏宇, 蒋世民, 贾欣燕, 樊代和 2023 物理学报 72 050301Google Scholar

    Zeng B Y, Gu P Y, Jiang S M, Jia X Y, Fan D H 2023 Acta Phys. Sin. 72 050301Google Scholar

    [13]

    Rivas Á, Huelga S F, Plenio M B 2014 Rep. Prog. Phys. 77 094001Google Scholar

    [14]

    Breuer H P, Laine E M, Piilo J, Vacchini B 2016 Rev. Mod. Phys. 88 021002Google Scholar

    [15]

    de Vicente J I, Spee C, Sauerwein D, Kraus B 2017 Phys. Rev. A 95 012323Google Scholar

    [16]

    Li L, Hall M J W, Wiseman H M 2018 Phys. Rep. 759 1Google Scholar

    [17]

    Weissman M B 1988 Rev. Mod. Phys. 60 537Google Scholar

    [18]

    Mi X, Cady J V, Zajac D M, Deelman P W, Petta J R 2017 Science 355 156Google Scholar

    [19]

    Groeblacher S, Trubarov A, Prigge N, Cole G D, Aspelmeyer M, Eisert J 2015 Nat. Commun. 6 7606Google Scholar

    [20]

    Potočnik A, Bargerbos A, Schröder F A Y N, Khan S A, Collodo M C, Gasparinetti S, Salathé Y, Creatore C, Eichler C, Türeci H E, Chin A W, Wallraff A 2018 Nat. Commun. 9 904Google Scholar

    [21]

    Haikka P, McEndoo S, De Chiara G, Palma G M, Maniscalco S 2011 Phys. Rev. A 84 031602Google Scholar

    [22]

    Utagi S, Srikanth R, Banerjee S 2020 Sci. Rep. 10 15049Google Scholar

    [23]

    Naikoo J, Banerjee S, Chandrashekar C M 2020 Phys. Rev. A 102 062209Google Scholar

    [24]

    Yu T, Eberly J 2007 Quantum Inf. Comput. 7 459Google Scholar

    [25]

    Kraus K 1971 Ann. Phys. 64 311Google Scholar

    [26]

    Rivas Á, Huelga S F, Plenio M B 2010 Phys. Rev. Lett. 105 050403Google Scholar

    [27]

    Breuer H P, Laine E M, Piilo J 2009 Phys. Rev. Lett. 103 210401Google Scholar

    [28]

    Pinto J P, Karpat G, Fanchini F F 2013 Phys. Rev. A. 88 034304Google Scholar

    [29]

    Yu T, Eberly J 2010 Opt. Commun. 283 676Google Scholar

    [30]

    Bellomo B, Franco R L, Compagno G 2007 Phys. Rev. Lett. 99 160502Google Scholar

    [31]

    Horodecki R, Horodecki P, Horodecki M 1995 Phys. Lett. A 200 340Google Scholar

  • [1] 于欣淼, 杨舒媛, 贺衎. 由任意多个独立的观察者共享Werner态的纠缠. 物理学报, 2023, 72(7): 070301. doi: 10.7498/aps.72.20222039
    [2] 曾柏云, 辜鹏宇, 蒋世民, 贾欣燕, 樊代和. Markov环境下“X”态基于CHSH不等式的量子非局域关联检验. 物理学报, 2023, 72(5): 050301. doi: 10.7498/aps.72.20222218
    [3] 贺志, 蒋登魁, 李艳. 一种与开放系统初态无关的非马尔科夫度量. 物理学报, 2022, 71(21): 210303. doi: 10.7498/aps.71.20221053
    [4] 张乐, 袁训锋, 谭小东. 退相位环境下Werner态在石墨烯基量子通道中的隐形传输. 物理学报, 2022, 71(7): 070304. doi: 10.7498/aps.71.20211881
    [5] 胡强, 曾柏云, 辜鹏宇, 贾欣燕, 樊代和. 退相干条件下两比特纠缠态的量子非局域关联检验. 物理学报, 2022, 71(7): 070301. doi: 10.7498/aps.71.20211453
    [6] 曾柏云, 辜鹏宇, 胡强, 贾欣燕, 樊代和. 基于CHSH不等式几何解释的“X”态量子非局域关联检验. 物理学报, 2022, 71(17): 170302. doi: 10.7498/aps.71.20220445
    [7] 张金峰, 阿拉帕提·阿不力米提, 杨帆, 艾克拜尔·阿木提江, 唐诗生, 艾合买提·阿不力孜. 不同外加磁场中Kaplan-Shekhtman-Entin-Wohlman-Aharony相互作用对量子失协非马尔科夫演化的影响. 物理学报, 2021, 70(22): 223401. doi: 10.7498/aps.70.20211277
    [8] 刘晋, 缪波, 贾欣燕, 樊代和. 基于Hardy-type佯谬的混合态高概率量子非局域关联检验. 物理学报, 2019, 68(23): 230302. doi: 10.7498/aps.68.20191125
    [9] 李金晴, 罗云荣, 海文华. 囚禁单离子的量子阻尼运动. 物理学报, 2017, 66(23): 233701. doi: 10.7498/aps.66.233701
    [10] 叶世强, 陈小余. 基于量子相干性的四体贝尔不等式构建. 物理学报, 2017, 66(20): 200301. doi: 10.7498/aps.66.200301
    [11] 黄江. 弱测量对四个量子比特量子态的保护. 物理学报, 2017, 66(1): 010301. doi: 10.7498/aps.66.010301
    [12] 游波, 岑理相. 非马尔科夫耗散系统长时演化下的极限环振荡现象. 物理学报, 2015, 64(21): 210302. doi: 10.7498/aps.64.210302
    [13] 杨光, 廉保旺, 聂敏. 振幅阻尼信道量子隐形传态保真度恢复机理. 物理学报, 2015, 64(1): 010303. doi: 10.7498/aps.64.010303
    [14] 刘莉, 徐伟, 岳晓乐, 韩群. 一类含非黏滞阻尼的Duffing单边碰撞系统的激变研究. 物理学报, 2013, 62(20): 200501. doi: 10.7498/aps.62.200501
    [15] 林方, 胡丹青, 李乐乐. 用一种分数阶算法研究非马尔可夫过程中阻尼与涨落的竞争机制. 物理学报, 2013, 62(12): 120503. doi: 10.7498/aps.62.120503
    [16] 赵加强, 曹连振, 逯怀新, 王晓芹. 三比特类GHZ态的Bell型不等式和非定域性. 物理学报, 2013, 62(12): 120301. doi: 10.7498/aps.62.120301
    [17] 蔡诚俊, 方卯发, 肖兴, 黄江. 非马尔可夫环境下经典场驱动Jaynes-Cummings模型中原子的熵压缩. 物理学报, 2012, 61(21): 210303. doi: 10.7498/aps.61.210303
    [18] 赵加强, 曹连振, 王晓芹, 逯怀新. 三光子GHZ态中不同Bell型不等式的实验研究. 物理学报, 2012, 61(17): 170301. doi: 10.7498/aps.61.170301
    [19] 刘其功, 计新. 相位阻尼通道下初始纠缠对纠缠演化的影响. 物理学报, 2012, 61(23): 230303. doi: 10.7498/aps.61.230303
    [20] 郑力明, 刘颂豪, 王发强. 非马尔可夫环境下原子的几何相位演化. 物理学报, 2009, 58(4): 2430-2434. doi: 10.7498/aps.58.2430
计量
  • 文章访问数:  1166
  • PDF下载量:  61
  • 被引次数: 0
出版历程
  • 收稿日期:  2024-03-31
  • 修回日期:  2024-06-19
  • 上网日期:  2024-07-16
  • 刊出日期:  2024-08-20

/

返回文章
返回