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

逾渗分立时间量子行走的传输及纠缠特性

安志云 李志坚

引用本文:
Citation:

逾渗分立时间量子行走的传输及纠缠特性

安志云, 李志坚

Properties of distribution and entanglement in discrete-time quantum walk with percolation

An Zhi-Yun, Li Zhi-Jian
PDF
导出引用
  • 在一维分立时间量子行走中,通过静态和动态两种方式随机地断开连接边引入无序效应,研究了静态逾渗和动态逾渗对量子行走传输特性以及位置自由度和硬币自由之间纠缠的影响.随着演化时间的增加,静态逾渗会使得量子行走从弹道传输转变为安德森局域化,而动态逾渗则会使之转变为经典扩散.理想情况下,量子纠缠在较短的时间内就达到一个常数值E0.静态逾渗量子行走的纠缠减小,并随着时间做无规振荡,而动态逾渗量子行走的纠缠则会随着时间光滑地增加,并在某一时间超过理想情况下的常数值,表现出动态逾渗增强量子纠缠的特性.
    We investigate one-dimensional discrete-time quantum walk on the line where the links between neighboring sites are randomly broken. Two link-broken ways, static percolation and dynamical percolation, are considered. The former means that the broken links are fixed in position space at each time step, while the latter is that broken links are varied with time step. Our attention focuses on the effects of these disorders on two physical quantities, the probability distribution and the entanglement between the coin degree of freedom and position degree of freedom. Choosing Hadamard coin operator and assuming the walker to start from the position eigenstate|0〉and attach itself to a coherent coin state 1/√2 (|↑〉+ i|↓〉), we give the statistical average results after making numerical calculations many times. The choices of coin operator and initial state, resulting in a symmetric probability distribution about origin in the ideal case, is helpful in comparing with different cases in different disorder strengths. It is shown that the probability distribution of static percolation quantum walk can change from a coherent behavior at short time to Anderson localization at longer time, while the dynamical percolation quantum walk can change to a classical diffusive behavior. With the decrease of the percolation probability, these transitions become faster. The entanglement for ideal case without disorder reaches a constant value after a short time evolution. The static percolation makes the entanglement less than that of ideal case and fluctuate irregularly around a certain value. The situation is very different for the dynamical percolation:the entanglement increases smoothly with the time step and can exceed the constant value in the ideal case at some time. Both of entanglements for two types of percolations decrease with reducing percolation probability. As a striking characteristic, the entanglement in dynamical case can tend to maximum regardless of percolation probability in long time limit, while the static case cannot. In the model for our study, the randomized unitary operations, induced by the static and dynamical percolations, can lead to some noticeable effects on the transport and entanglement of discrete time quantum walk. The results about the interplay between disorder and entanglement not only assist quantum information processing, but also give more options to further explore and understand disorder physical processes in nature.
      通信作者: 李志坚, zjli@sxu.edu.cn
    • 基金项目: 山西省回国留学人员科研资助项目(批准号:2015-012)和山西省面上自然科学基金(批准号:201601D011009)资助的课题.
      Corresponding author: Li Zhi-Jian, zjli@sxu.edu.cn
    • Funds: Project supported by Shanxi Scholarship Council of China (Grant No.2015-012),and Natural Science Foundation of Shanxi Province,China (Grant No.201601D011009).
    [1]

    Farhi E, Gutmann S 1998 Phys. Rev. A 58 915

    [2]

    Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687

    [3]

    Chandrashekar C M 2013 Sci. Rep. 3 2829

    [4]

    Kempe J 2003 Contemp. Phys. 44 307

    [5]

    Zaburdaev V, Denisov S, Klafter J 2015 Rev. Mod. Phys. 87 483

    [6]

    Ambainis A 2003 Int. J. Quantum Inf. 1 507518

    [7]

    Childs A M, Gosset D, Webb Z 2013 Science 339 791

    [8]

    Du J, Li H, Xu X, Shi M, Wu J, Zhou X, Han R 2003 Phys. Rev. A 67 042316

    [9]

    Schmitz H, Matjeschk R, Schneider Ch, Glueckert J, Enderlein M, Huber T, Schaetz T 2009 Phys. Rev. Lett. 103 090504

    [10]

    Karski M, Forster L, Choi J M, Steffen A, Alt W, Meschede D, Widera A 2009 Science 325 174

    [11]

    Xue P, Qin H, Tang B, Zhan X, Bian Z H, Li J 2014 Chin. Phys. B 23 110307

    [12]

    Engel G S, Calhoun T R, Read E L 2007 Nature 446 782

    [13]

    Chandrashekar C M 2011 Phys. Rev. A 83 022320

    [14]

    Kitagawa T, Rudner M S, Berg E 2010 Phys. Rev. A 82 033429

    [15]

    Beggi A, Buscemi F, Bordone P 2016 Quantum Inf. Process. 15 3711

    [16]

    Li Z J, Wang J B 2015 Sci. Rep. 5 13585

    [17]

    Wang L, Wang L, Zhang Y 2014 Phys. Rev. A 90 063618

    [18]

    Wang Q H, Li Z J 2016 Ann. Phys. 373 1

    [19]

    Di Franco C, Mc Gettrick M, Busch T 2011 Phys. Rev. Lett. 106 080502

    [20]

    Goyal S K, Chandrashekar C M 2010 J. Phys. A:Math. Theor. 43 235303

    [21]

    Carneiro I, Loo M, Xu X 2005 New J. Phys. 7 156

    [22]

    Vieira R, Amorim E P M, Rigolin G 2014 Phys. Rev. A 89 042307

    [23]

    Vieira R, Amorim E P M, Rigolin G 2013 Phys. Rev. Lett. 111 180503

    [24]

    Chandrashekar C M 2012 arXiv:12125984v1

    [25]

    Li Z J, Izaac J A, Wang J B 2013 Phys. Rev. A 87 012314

    [26]

    Yin Y, Katsanos D E, Evangelou S N 2008 Phys. Rev. A 77 022302

    [27]

    Schreiber A, Cassemiro K N, Potocek V, Gabris A, Jex I, Silberhorn C 2011 Phys. Rev. Lett. 106 180403

    [28]

    Törmä P, Jex I, Schleich W P 2002 Phys. Rev. A 65 052110

    [29]

    Chou C I, Ho C L 2014 Chin. Phys. B 23 110302

    [30]

    Wang D D, Li Z J 2016 Acta Phys. Sin. 65 060301 (in Chinese)[王丹丹, 李志坚 2016 物理学报 65 060301]

    [31]

    Lam H T, Szeto K Y 2015 Phys. Rev. A 92 012323

    [32]

    Bennett C H, Bernstein H J, Popescu S 1996 Phys. Rev. A 53 2046

  • [1]

    Farhi E, Gutmann S 1998 Phys. Rev. A 58 915

    [2]

    Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687

    [3]

    Chandrashekar C M 2013 Sci. Rep. 3 2829

    [4]

    Kempe J 2003 Contemp. Phys. 44 307

    [5]

    Zaburdaev V, Denisov S, Klafter J 2015 Rev. Mod. Phys. 87 483

    [6]

    Ambainis A 2003 Int. J. Quantum Inf. 1 507518

    [7]

    Childs A M, Gosset D, Webb Z 2013 Science 339 791

    [8]

    Du J, Li H, Xu X, Shi M, Wu J, Zhou X, Han R 2003 Phys. Rev. A 67 042316

    [9]

    Schmitz H, Matjeschk R, Schneider Ch, Glueckert J, Enderlein M, Huber T, Schaetz T 2009 Phys. Rev. Lett. 103 090504

    [10]

    Karski M, Forster L, Choi J M, Steffen A, Alt W, Meschede D, Widera A 2009 Science 325 174

    [11]

    Xue P, Qin H, Tang B, Zhan X, Bian Z H, Li J 2014 Chin. Phys. B 23 110307

    [12]

    Engel G S, Calhoun T R, Read E L 2007 Nature 446 782

    [13]

    Chandrashekar C M 2011 Phys. Rev. A 83 022320

    [14]

    Kitagawa T, Rudner M S, Berg E 2010 Phys. Rev. A 82 033429

    [15]

    Beggi A, Buscemi F, Bordone P 2016 Quantum Inf. Process. 15 3711

    [16]

    Li Z J, Wang J B 2015 Sci. Rep. 5 13585

    [17]

    Wang L, Wang L, Zhang Y 2014 Phys. Rev. A 90 063618

    [18]

    Wang Q H, Li Z J 2016 Ann. Phys. 373 1

    [19]

    Di Franco C, Mc Gettrick M, Busch T 2011 Phys. Rev. Lett. 106 080502

    [20]

    Goyal S K, Chandrashekar C M 2010 J. Phys. A:Math. Theor. 43 235303

    [21]

    Carneiro I, Loo M, Xu X 2005 New J. Phys. 7 156

    [22]

    Vieira R, Amorim E P M, Rigolin G 2014 Phys. Rev. A 89 042307

    [23]

    Vieira R, Amorim E P M, Rigolin G 2013 Phys. Rev. Lett. 111 180503

    [24]

    Chandrashekar C M 2012 arXiv:12125984v1

    [25]

    Li Z J, Izaac J A, Wang J B 2013 Phys. Rev. A 87 012314

    [26]

    Yin Y, Katsanos D E, Evangelou S N 2008 Phys. Rev. A 77 022302

    [27]

    Schreiber A, Cassemiro K N, Potocek V, Gabris A, Jex I, Silberhorn C 2011 Phys. Rev. Lett. 106 180403

    [28]

    Törmä P, Jex I, Schleich W P 2002 Phys. Rev. A 65 052110

    [29]

    Chou C I, Ho C L 2014 Chin. Phys. B 23 110302

    [30]

    Wang D D, Li Z J 2016 Acta Phys. Sin. 65 060301 (in Chinese)[王丹丹, 李志坚 2016 物理学报 65 060301]

    [31]

    Lam H T, Szeto K Y 2015 Phys. Rev. A 92 012323

    [32]

    Bennett C H, Bernstein H J, Popescu S 1996 Phys. Rev. A 53 2046

  • [1] 刘腾, 陆鹏飞, 胡碧莹, 吴昊, 劳祺峰, 边纪, 刘泱, 朱峰, 罗乐. 离子阱中以声子为媒介的多体量子纠缠与逻辑门. 物理学报, 2022, 71(8): 080301. doi: 10.7498/aps.71.20220360
    [2] 宋悦, 李军奇, 梁九卿. 级联环境下三量子比特量子关联动力学研究. 物理学报, 2021, 70(10): 100301. doi: 10.7498/aps.70.20202133
    [3] 张诗豪, 张向东, 李绿周. 基于测量的量子计算研究进展. 物理学报, 2021, 70(21): 210301. doi: 10.7498/aps.70.20210923
    [4] 仲银银, 潘晓州, 荆杰泰. 级联四波混频相干反馈控制系统量子纠缠特性. 物理学报, 2020, 69(13): 130301. doi: 10.7498/aps.69.20200042
    [5] 李海, 邹健, 邵彬, 陈雨, 华臻. 库的量子关联相干辅助系统能量提取的研究. 物理学报, 2019, 68(4): 040201. doi: 10.7498/aps.68.20181525
    [6] 许鹏, 何晓东, 刘敏, 王谨, 詹明生. 中性原子量子计算研究进展. 物理学报, 2019, 68(3): 030305. doi: 10.7498/aps.68.20182133
    [7] 任志红, 李岩, 李艳娜, 李卫东. 基于量子Fisher信息的量子计量进展. 物理学报, 2019, 68(4): 040601. doi: 10.7498/aps.68.20181965
    [8] 杨荣国, 张超霞, 李妮, 张静, 郜江瑞. 级联四波混频系统中纠缠增强的量子操控. 物理学报, 2019, 68(9): 094205. doi: 10.7498/aps.68.20181837
    [9] 李雪琴, 赵云芳, 唐艳妮, 杨卫军. 基于金刚石氮-空位色心自旋系综与超导量子电路混合系统的量子节点纠缠. 物理学报, 2018, 67(7): 070302. doi: 10.7498/aps.67.20172634
    [10] 王灿灿. 量子纠缠与宇宙学弗里德曼方程. 物理学报, 2018, 67(17): 179501. doi: 10.7498/aps.67.20180813
    [11] 苏耀恒, 陈爱民, 王洪雷, 相春环. 一维自旋1键交替XXZ链中的量子纠缠和临界指数. 物理学报, 2017, 66(12): 120301. doi: 10.7498/aps.66.120301
    [12] 丛美艳, 杨晶, 黄燕霞. 在不同初态下Dzyaloshinskii-Moriya相互作用及内禀退相干对海森伯系统的量子纠缠的影响. 物理学报, 2016, 65(17): 170301. doi: 10.7498/aps.65.170301
    [13] 夏建平, 任学藻, 丛红璐, 王旭文, 贺树. 两量子比特与谐振子相耦合系统中的量子纠缠演化特性. 物理学报, 2012, 61(1): 014208. doi: 10.7498/aps.61.014208
    [14] 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
    [15] 刘圣鑫, 李莎莎, 孔祥木. Dzyaloshinskii-Moriya相互作用对量子XY链中热纠缠的影响. 物理学报, 2011, 60(3): 030303. doi: 10.7498/aps.60.030303
    [16] 陈宇, 邹健, 李军刚, 邵彬. 耗散环境下三原子之间稳定纠缠的量子反馈控制. 物理学报, 2010, 59(12): 8365-8370. doi: 10.7498/aps.59.8365
    [17] 周南润, 曾宾阳, 王立军, 龚黎华. 基于纠缠的选择自动重传量子同步通信协议. 物理学报, 2010, 59(4): 2193-2199. doi: 10.7498/aps.59.2193
    [18] 姚志欣, 钟建伟, 毛邦宁, 陈 钢, 潘佰良. 双孔干涉效应的量子描述. 物理学报, 2007, 56(6): 3185-3191. doi: 10.7498/aps.56.3185
    [19] 胡要花, 方卯发, 廖湘萍, 郑小娟. 二项式光场与级联三能级原子的量子纠缠. 物理学报, 2006, 55(9): 4631-4637. doi: 10.7498/aps.55.4631
    [20] 王成志, 方卯发. 双模压缩真空态与原子相互作用中的量子纠缠和退相干. 物理学报, 2002, 51(9): 1989-1995. doi: 10.7498/aps.51.1989
计量
  • 文章访问数:  2824
  • PDF下载量:  183
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-12-18
  • 修回日期:  2017-04-01
  • 刊出日期:  2017-07-05

逾渗分立时间量子行走的传输及纠缠特性

  • 1. 山西大学理论物理研究所, 太原 030006
  • 通信作者: 李志坚, zjli@sxu.edu.cn
    基金项目: 山西省回国留学人员科研资助项目(批准号:2015-012)和山西省面上自然科学基金(批准号:201601D011009)资助的课题.

摘要: 在一维分立时间量子行走中,通过静态和动态两种方式随机地断开连接边引入无序效应,研究了静态逾渗和动态逾渗对量子行走传输特性以及位置自由度和硬币自由之间纠缠的影响.随着演化时间的增加,静态逾渗会使得量子行走从弹道传输转变为安德森局域化,而动态逾渗则会使之转变为经典扩散.理想情况下,量子纠缠在较短的时间内就达到一个常数值E0.静态逾渗量子行走的纠缠减小,并随着时间做无规振荡,而动态逾渗量子行走的纠缠则会随着时间光滑地增加,并在某一时间超过理想情况下的常数值,表现出动态逾渗增强量子纠缠的特性.

English Abstract

参考文献 (32)

目录

    /

    返回文章
    返回