基于量子相干性的四体贝尔不等式构建

叶世强; 陈小余

doi:10.7498/aps.66.200301

摘要

贝尔不等式在定域性和实在性的双重假设下，对于被分隔的粒子同时被测量时其结果的可能关联程度建立了一个严格的限制，违反贝尔不等式确保量子态存在纠缠.本文利用量子相干性的l1和相对熵测度构建了四体量子贝尔不等式，发现一般实系数Greenberger-Horne-Zeilinger纯态和簇纯态总是违反四体相对熵相干性测度贝尔不等式，因此违反四体相对熵相干性测度贝尔不等式的这些态是纠缠态.

关键词:

It is well known that Bell inequalities are derived under the assumptions of locality and realism. Bell inequalities impose strict constraints on the statistical correlations of measurements of multipartite systems. Violating each of them guarantees the existence of quantum correlations in a quantum state. A quantum state with non-vanishing entanglement may violate some Bell inequalities. Recent progress of the fields like quantum biology and quantum thermodynamics reveals a particular role of quantum coherence in quantum information processing. Quantum coherence is identified by the presence of off-diagonal terms in the density matrix. To quantify quantum coherence of a given state, Baumgratz et al. (Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401) provided several kinds of coherence measures such as l1-norm of coherence and relative entropy of coherence. In this paper, we propose to use quantum coherence to derive Bell inequalities. We construct the Bell inequalities of four-partite product states with l1-norm of coherence, relative entropy of coherence. In the Bell inequalities of four-partite correlations, measurement operators are products of local measurement operators. Each local operator is one of the two arbitrary observables. We consider the violations of the four-partite Bell inequalities by the four-partite general pure Greenberger-Horne-Zeilinger (GHZ) state, cluster states, W states with real coefficients. We also investigate the violations of the four-partite Bell inequalities by the four-partite GHZ class mixed states, cluster class mixed states, W class mixed states and Dicke class mixed states. It is shown that the four-partite Bell inequalities in terms of relative entropy of coherence are always violated by the four-partite general pure GHZ states, cluster states with the real coefficients. Hence there is non-vanishing entanglement for these states.

Keywords:

作者及机构信息

1.
浙江工商大学信息与电子工程学院, 杭州 310018

通信作者: 陈小余, xychen@zjgsu.edu.cn

基金项目: 国家自然科学基金（批准号：11375152）资助的课题.

Authors and contacts

1.
College of Information and Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, China

Corresponding author: Chen Xiao-Yu, xychen@zjgsu.edu.cn

Funds: Project support by the National Natural Science Foundation of China (Grant No. 11375152).

参考文献

[1]	Bell J S 1964 Physics 1 195
[2]	Greenberger D M, Horne M A, Shimony A, Zeilinger A, Am J 1990 Physica 58 1131
[3]	Clauser J F, Horne M A, Shimony A, Holt R A 1969 Phys. Rev. Lett. 23 880
[4]	Mermin N D 1990 Phys. Rev. Lett. 65 1838
[5]	Ardehali M 1992 Phys. Rev. A 46 5375
[6]	BelinskiiAV, Klyshko D N 1993 Phys. Usp. 36 653
[7]	Peres A 1999 Found. Phys. 29 589
[8]	Pitowsky I, Svozil K 2001 Phys. Rev. A 64 014102
[9]	Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865
[10]	Wang X Q, Lu H X, Zhao J Q 2011 Acta Phys. Sin. 60 110301 (in Chinese)[王晓芹, 逯怀新, 赵加强2011 60 110301]
[11]	Chen J L, Wu C F, Kwek L C, Oh C H 2004 Phys. Rev. Lett. 93 140407
[12]	Yu S X, Chen Q, Zhang C J, Lai C H, Oh C H 2012 Phys. Rev. Lett. 109 120402
[13]	Gisin N 1991 Phys. Lett. A 154 201
[14]	Gisin N, Peres A 1992 Phys. Lett. A 162 15
[15]	Silva R, Gisin N, Guryanova Y, Popescu S 2015 Phys. Rev. Lett. 114 250401
[16]	Gisin N 2015 arXiv:1509.00767
[17]	Gisin N, Tanzilli S, Tittel W 2015 Europhys. News 46 36
[18]	Ptz G, Aktas D, Martin A, Fedrici B, Tanzilli S, Gisin N 2016 Phys. Rev. Lett. 116 010401
[19]	Xie L J, Zhang D Y, Wang X W, Zhan X G, Tang S Q, Gao F 2011 Chin. Phys. B 20 080301
[20]	Zukowski M, Brukner C 2002 Phys. Rev. Lett. 88 210401
[21]	Sen A, Sen U, Zukowski M 2002 Phys. Rev. A 66 062318
[22]	Zhao J Q, Cao L Z, Lu H X, Wang X Q 2013 Acta Phys. Sin. 62 120301 (in Chinese)[赵加强, 曹连振, 逯怀新, 王晓芹2013 62 120301]
[23]	Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401
[24]	Girolami D 2014 Phys. Rev. Lett. 113 170401
[25]	Sreltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403
[26]	Mondal D, Pramanik T, Pati A K 2017 Phys. Rev. A 95 010301
[27]	Abbott D, Davies P, Pati A K 2008 Quantum Aspects of Life (London:Imperial College Press)
[28]	Plenio M B, Huelga S F 2008 New J. Phys. 10 113019
[29]	Rebentrost P, Mohseni M, Aspuru-Guzik A 2009 J. Phys. Chem. B 113 9942
[30]	Lloyd S 2011 J. Phys. Conf. Ser. 302 012037
[31]	Huelga S, Plenio M 2013 Contemp. Phys. 54 181
[32]	Rodrıguez-Rosario C A, Frauenheim T, Aspuru-GuzikA 2013 arXiv:1308.1245
[33]	Lostaglio M, Jennings D, Rudolph T 2015 Nat. Commun. 6 6383
[34]	Narasimhachar V, Gour G 2015 Nat. Commun. 6 7689
[35]	Lostaglio M, Korzekwa K, Jennings D, Rudolph T 2015 Phys. Rev. X 5 021001
[36]	Gardas B, Deffner S 2015 Phys. Rev. E 92 042126
[37]	Singh U, Bera M N, Misra A, Pati A K 2015 arXiv:1506.08186
[38]	Winter A, Yang D 2016 Phys. Rev. Lett. 116 120404
[39]	Singh U, Bera M N, Dhar H S, Pati A K 2015 Phys. Rev. A 91 052115
[40]	Kumar A 2017 Phys. Lett. A 381 991
[41]	Xi Z J, Li Y M, Fan H 2015 Sci. Rep. 5 10922
[42]	Yao Y, Xiao X, Ge L, Sun C P 2015 Phys. Rev. A 92 022112
[43]	Cheng S, Hall M J W 2015 Phys. Rev. A 92 042101
[44]	Bu K F, Kumar A, Wu J D 2016 arXiv:1603.06322
[45]	Qiu L, Liu Z, Pan F 2016 arXiv:1610.07237
[46]	Dr W, Vidal G, Cirac J I 2000 Phys. Rev. A 62 062314
[47]	Chen X Y, Wang T T 2015 Chin. Phys. B 24 080303
[48]	Ghne O, Jungnitsch B, Moroder T, Weinstein Y S 2011 Phys. Rev. A 84 052319
[49]	KhosaA H, Saif F 2010 Chin. Phys. B 19 040309
[50]	Kiesel N, Schmid C, Tth G, Solano E, Weinfurter H 2007 Phys. Rev. Lett. 98 063604
[51]	Chen J L, Su H Y, Xu Z P, Wu Y C, Wu C F, Ye X J, Zukowski M, Kwek L C 2015 Sci. Reports 5 11624
[52]	Xu J Z, Guo J B, Wen W, Bai Y K, Yan F L 2012 Chin. Phys. B 21 080305
[53]	PittengerA O, Rubin M H 2000 Opt.Commun. 179 447
[54]	Napoli C, Bromley T R, Cianciaruso M, Piani M, Johnston N, Adesso G 2016 Phys. Rev. Lett. 116 150502

施引文献

[1]	Bell J S 1964 Physics 1 195
[2]	Greenberger D M, Horne M A, Shimony A, Zeilinger A, Am J 1990 Physica 58 1131
[3]	Clauser J F, Horne M A, Shimony A, Holt R A 1969 Phys. Rev. Lett. 23 880
[4]	Mermin N D 1990 Phys. Rev. Lett. 65 1838
[5]	Ardehali M 1992 Phys. Rev. A 46 5375
[6]	BelinskiiAV, Klyshko D N 1993 Phys. Usp. 36 653
[7]	Peres A 1999 Found. Phys. 29 589
[8]	Pitowsky I, Svozil K 2001 Phys. Rev. A 64 014102
[9]	Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865
[10]	Wang X Q, Lu H X, Zhao J Q 2011 Acta Phys. Sin. 60 110301 (in Chinese)[王晓芹, 逯怀新, 赵加强2011 60 110301]
[11]	Chen J L, Wu C F, Kwek L C, Oh C H 2004 Phys. Rev. Lett. 93 140407
[12]	Yu S X, Chen Q, Zhang C J, Lai C H, Oh C H 2012 Phys. Rev. Lett. 109 120402
[13]	Gisin N 1991 Phys. Lett. A 154 201
[14]	Gisin N, Peres A 1992 Phys. Lett. A 162 15
[15]	Silva R, Gisin N, Guryanova Y, Popescu S 2015 Phys. Rev. Lett. 114 250401
[16]	Gisin N 2015 arXiv:1509.00767
[17]	Gisin N, Tanzilli S, Tittel W 2015 Europhys. News 46 36
[18]	Ptz G, Aktas D, Martin A, Fedrici B, Tanzilli S, Gisin N 2016 Phys. Rev. Lett. 116 010401
[19]	Xie L J, Zhang D Y, Wang X W, Zhan X G, Tang S Q, Gao F 2011 Chin. Phys. B 20 080301
[20]	Zukowski M, Brukner C 2002 Phys. Rev. Lett. 88 210401
[21]	Sen A, Sen U, Zukowski M 2002 Phys. Rev. A 66 062318
[22]	Zhao J Q, Cao L Z, Lu H X, Wang X Q 2013 Acta Phys. Sin. 62 120301 (in Chinese)[赵加强, 曹连振, 逯怀新, 王晓芹2013 62 120301]
[23]	Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401
[24]	Girolami D 2014 Phys. Rev. Lett. 113 170401
[25]	Sreltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403
[26]	Mondal D, Pramanik T, Pati A K 2017 Phys. Rev. A 95 010301
[27]	Abbott D, Davies P, Pati A K 2008 Quantum Aspects of Life (London:Imperial College Press)
[28]	Plenio M B, Huelga S F 2008 New J. Phys. 10 113019
[29]	Rebentrost P, Mohseni M, Aspuru-Guzik A 2009 J. Phys. Chem. B 113 9942
[30]	Lloyd S 2011 J. Phys. Conf. Ser. 302 012037
[31]	Huelga S, Plenio M 2013 Contemp. Phys. 54 181
[32]	Rodrıguez-Rosario C A, Frauenheim T, Aspuru-GuzikA 2013 arXiv:1308.1245
[33]	Lostaglio M, Jennings D, Rudolph T 2015 Nat. Commun. 6 6383
[34]	Narasimhachar V, Gour G 2015 Nat. Commun. 6 7689
[35]	Lostaglio M, Korzekwa K, Jennings D, Rudolph T 2015 Phys. Rev. X 5 021001
[36]	Gardas B, Deffner S 2015 Phys. Rev. E 92 042126
[37]	Singh U, Bera M N, Misra A, Pati A K 2015 arXiv:1506.08186
[38]	Winter A, Yang D 2016 Phys. Rev. Lett. 116 120404
[39]	Singh U, Bera M N, Dhar H S, Pati A K 2015 Phys. Rev. A 91 052115
[40]	Kumar A 2017 Phys. Lett. A 381 991
[41]	Xi Z J, Li Y M, Fan H 2015 Sci. Rep. 5 10922
[42]	Yao Y, Xiao X, Ge L, Sun C P 2015 Phys. Rev. A 92 022112
[43]	Cheng S, Hall M J W 2015 Phys. Rev. A 92 042101
[44]	Bu K F, Kumar A, Wu J D 2016 arXiv:1603.06322
[45]	Qiu L, Liu Z, Pan F 2016 arXiv:1610.07237
[46]	Dr W, Vidal G, Cirac J I 2000 Phys. Rev. A 62 062314
[47]	Chen X Y, Wang T T 2015 Chin. Phys. B 24 080303
[48]	Ghne O, Jungnitsch B, Moroder T, Weinstein Y S 2011 Phys. Rev. A 84 052319
[49]	KhosaA H, Saif F 2010 Chin. Phys. B 19 040309
[50]	Kiesel N, Schmid C, Tth G, Solano E, Weinfurter H 2007 Phys. Rev. Lett. 98 063604
[51]	Chen J L, Su H Y, Xu Z P, Wu Y C, Wu C F, Ye X J, Zukowski M, Kwek L C 2015 Sci. Reports 5 11624
[52]	Xu J Z, Guo J B, Wen W, Bai Y K, Yan F L 2012 Chin. Phys. B 21 080305
[53]	PittengerA O, Rubin M H 2000 Opt.Commun. 179 447
[54]	Napoli C, Bromley T R, Cianciaruso M, Piani M, Johnston N, Adesso G 2016 Phys. Rev. Lett. 116 150502

[1]	郭牧城, 汪福东, 胡肇高, 任苗苗, 孙伟业, 肖婉婷, 刘书萍, 钟满金. 微纳尺度稀土掺杂晶体的量子相干性能及其应用研究进展. , 2023, 72(12): 120302. doi: 10.7498/aps.72.20222166
[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. , 2023, 72(5): 050301. doi: 10.7498/aps.72.20222218
[3]	蔚娟, 张岩, 吴银花, 杨文海, 闫智辉, 贾晓军. 双模压缩态量子相干性演化的实验研究. , 2023, 72(3): 034202. doi: 10.7498/aps.72.20221923
[4]	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. , 2022, 71(17): 170302. doi: 10.7498/aps.71.20220445
[5]	董曜, 纪爱玲, 张国锋. 关联退极化量子信道中qutrit-qutrit系统的量子相干性演化. , 2022, 71(7): 070303. doi: 10.7498/aps.71.20212067
[6]	杨阳, 王安民, 曹连振, 赵加强, 逯怀新. 与XY双自旋链耦合的双量子比特系统的关联性与相干性. , 2018, 67(15): 150302. doi: 10.7498/aps.67.20180812
[7]	伊天成, 丁悦然, 任杰, 王艺敏, 尤文龙. 具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性. , 2018, 67(14): 140303. doi: 10.7498/aps.67.20172755
[8]	林银, 黄明达, 於亚飞, 张智明. 从离散Wigner函数的角度探讨量子相干性度量. , 2017, 66(11): 110301. doi: 10.7498/aps.66.110301
[9]	陈俊, 於亚飞, 张智明. 利用信息流方法优化多激发自旋链中的量子态传输. , 2015, 64(16): 160305. doi: 10.7498/aps.64.160305
[10]	贺志, 李莉, 姚春梅, 李艳. 利用量子相干性判定开放二能级系统中非马尔可夫性. , 2015, 64(14): 140302. doi: 10.7498/aps.64.140302
[11]	杨丽君, 马腾, 孙克家, 冯晓敏. 微波场作用下三能级原子系统的无反转光放大. , 2015, 64(6): 064205. doi: 10.7498/aps.64.064205
[12]	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. , 2013, 62(12): 120301. doi: 10.7498/aps.62.120301
[13]	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. , 2012, 61(17): 170301. doi: 10.7498/aps.61.170301
[14]	赵加强, 逯怀新. 原子偶极压缩的相干控制和Cauchy-Schwarz不等式的破坏. , 2010, 59(11): 7875-7879. doi: 10.7498/aps.59.7875
[15]	马瑞琼, 李永放, 时坚. 量子态的非相干光时域测量. , 2008, 57(9): 5593-5599. doi: 10.7498/aps.57.5593
[16]	王少凯, 任继刚, 金贤敏, 杨彬, 杨冬, 彭承志, 蒋硕, 王向斌. 自由空间量子通讯实验中纠缠源的研制. , 2008, 57(3): 1356-1359. doi: 10.7498/aps.57.1356
[17]	郭德军, 单传家, 夏云杰. 内禀退相干下Tavis-Cummings模型中原子的纠缠演化与贝尔不等式破坏. , 2007, 56(4): 2139-2147. doi: 10.7498/aps.56.2139
[18]	贾晓军, 苏晓龙, 潘庆, 谢常德, 彭堃墀. 具有经典相干性的两组EPR纠缠态光场的实验产生. , 2005, 54(6): 2717-2722. doi: 10.7498/aps.54.2717
[19]	郝三如, 王麓雅. 用外加驱动场压缩有热槽相互作用二态量子系统的退相干性. , 2000, 49(4): 610-614. doi: 10.7498/aps.49.610
[20]	印建平, 朱士群, 高伟建, 王育竹. 双模激光场的二阶量子相干性及其时谱特性. , 1995, 44(1): 72-79. doi: 10.7498/aps.44.72

计量

文章访问数: 6129
PDF下载量: 281
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板