Quantum nonlocality of generic family of four-qubit entangled pure states

doi:10.1088/1674-1056/24/7/070301

中国物理B ›› 2015, Vol. 24 ›› Issue (7): 70301-070301.doi: 10.1088/1674-1056/24/7/070301

Quantum nonlocality of generic family of four-qubit entangled pure states

丁东^{a b}, 何英秋^a, 闫凤利^a, 高亭^c

a College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050024, China;
b Department of Basic Curriculum, North China Institute of Science and Technology, Beijing 101601, China;
c College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China

收稿日期:2014-12-03 修回日期:2015-03-09 出版日期:2015-07-05 发布日期:2015-07-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11475054 and 11371005), Hebei Natural Science Foundation of China (Grant Nos. A2012205013 and A2014205060), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant Nos. 3142014068 and 3142014125), and Langfang Key Technology Research and Development Program of China (Grant No. 2014011002).

Quantum nonlocality of generic family of four-qubit entangled pure states

Ding Dong (丁东)^{a b}, He Ying-Qiu (何英秋)^a, Yan Feng-Li (闫凤利)^a, Gao Ting (高亭)^c

a College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050024, China;
b Department of Basic Curriculum, North China Institute of Science and Technology, Beijing 101601, China;
c College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China

Received:2014-12-03 Revised:2015-03-09 Online:2015-07-05 Published:2015-07-05
Contact: Yan Feng-Li, Gao Ting E-mail:flyan@hebtu.edu.cn;gaoting@hebtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11475054 and 11371005), Hebei Natural Science Foundation of China (Grant Nos. A2012205013 and A2014205060), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant Nos. 3142014068 and 3142014125), and Langfang Key Technology Research and Development Program of China (Grant No. 2014011002).

摘要/Abstract

摘要：

We directly introduce a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states |G_abcd> [Phys. Rev. A 65 052112 (2002)] and several canonical four-qubit entangled states. It has been demonstrated that the inequality is maximally violated by the so called “four-qubit the maximally entangled state |G_m>” and it is also violated by four-qubit W state and a special family of states |G_ab00>. Moreover, a useful entanglement-nonlocality relationship for the family of states |G_ab00> is derived. Finally, we present a scheme of preparation of the state |G_m ightangle with linear optics and cross-Kerr nonlinearities.

关键词: quantum nonlocality, Bell-type inequality, quantum entanglement

Abstract:

Key words: quantum nonlocality, Bell-type inequality, quantum entanglement

中图分类号: (Entanglement and quantum nonlocality)

03.65.Ud

03.67.-a (Quantum information) 03.67.Mn (Entanglement measures, witnesses, and other characterizations)

丁东, 何英秋, 闫凤利, 高亭. Quantum nonlocality of generic family of four-qubit entangled pure states[J]. 中国物理B, 2015, 24(7): 70301-070301.

Ding Dong (丁东), He Ying-Qiu (何英秋), Yan Feng-Li (闫凤利), Gao Ting (高亭). Quantum nonlocality of generic family of four-qubit entangled pure states[J]. Chin. Phys. B, 2015, 24(7): 70301-070301.

参考文献 52

[1]	Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[2]	Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[3]	Yan F L, Gao T and Chitambar E 2011 Phys. Rev. A 83 022319
[4]	Gao T, Yan F L and van Enk S J 2014 Phys. Rev. Lett. 112 180501
[5]	Bai Y K, Xu Y F and Wang Z D 2014 Phys. Rev. Lett. 113 100503
[6]	Ma Z H, Chen Z H, Chen J L, Spengler C, Gabriel A and Huber M 2011 Phys. Rev. A 83 062325
[7]	Hong Y, Gao T and Yan F L 2012 Phys. Rev. A 86 062323
[8]	Gao T and Hong Y 2011 Eur. Phys. J. D 61 765
[9]	Gao T and Hong Y 2010 Phys. Rev. A 82 062113
[10]	Dür W, Vidal G and Cirac J I 2000 Phys. Rev. A 62 062314
[11]	Acín A, Andrianov A, Costa L, Jané E, Latorre J I and Tarrach R 2000 Phys. Rev. Lett. 85 1560
[12]	Verstraete F, Dehaene J, De Moor B and Verschelde H 2002 Phys. Rev. A 65 052112
[13]	Liu B, Li J L, Li X K and Qiao C F 2012 Phys. Rev. Lett. 108 050501
[14]	Wootters W K 1998 Phys. Rev. Lett. 80 2245
[15]	Coffman V, Kundu J and Wootters W K 2000 Phys. Rev. A 61 052306
[16]	Sharma S S and Sharma N K 2010 Phys. Rev. A 82 012340
[17]	Sharma S S and Sharma N K 2013 Phys. Rev. A 87 022335
[18]	Sharma S S and Sharma N K arXiv:quant-ph/1309.2713
[19]	Wong A and Christensen N 2001 Phys. Rev. A 63 044301
[20]	Li D F, Li X R, Huang H T and Li X X 2009 J. Math. Phys. 50 012104
[21]	Bell J S 1987 Speakable and Unspeakable in Quantum Mechanics (Cambridge: Cambridge University Press)
[22]	Clauser J F, Horne M A, Shimony A and Holt R A 1969 Phys. Rev. Lett. 23 880
[23]	Gisin N 1991 Phys. Lett. A 154 201
[24]	Gisin N and Peres A 1992 Phys. Lett. A 162 15
[25]	Acín A, Chen J L, Gisin N, Kaszlikowski D, Kwek L C, Oh C H and Żukowski M 2004 Phys. Rev. Lett. 92 250404
[26]	Mermin N D 1990 Phys. Rev. Lett. 65 1838
[27]	Ardehali M 1992 Phys. Rev. A 46 5375
[28]	Belinskiï A V and Klyshko D N 1993 Phys. Usp. 36 653
[29]	Werner R F and Wolf M M 2001 Phys. Rev. A 64 032112
[30]	Żukowski M and Brukner Č 2002 Phys. Rev. Lett. 88 210401
[31]	Svetlichny G 1987 Phys. Rev. D 35 3066
[32]	Li M and Fei S M 2012 Phys. Rev. A 86 052119
[33]	Grandjean B, Liang Y C, Bancal J D, Brunner N and Gisin N 2012 Phys. Rev. A 85 052113
[34]	Scarani V, Acín A, Schenck E and Aspelmeyer M 2005 Phys. Rev. A 71 042325
[35]	Wu C F, Yeo Y, Kwek L C and Oh C H 2007 Phys. Rev. A 75 032332
[36]	Pitowsky I and Svozil K 2001 Phys. Rev. A 64 014102
[37]	Wu Y C, Żukowski M, Chen J L and Guo G C 2013 Phys. Rev. A 88 022126
[38]	Nemoto K and Munro W J 2004 Phys. Rev. Lett. 93 250502
[39]	Ding D, Yan F L and Gao T 2013 J. Opt. Soc. Am. B 30 003075
[40]	Yeo Y and Chua W K 2006 Phys. Rev. Lett. 96 060502
[41]	Higuchi A and Sudbery A 2000 Phys. Lett. A 273 213
[42]	Brown I D K, Stepney S, Sudbery A and Braunstein S L 2005 J. Phys. A 38 1119
[43]	Ghose S, Sinclair N, Debnath S, Rungta P and Stock R 2009 Phys. Rev. Lett. 102 250404
[44]	Ajoy A and Rungta P 2010 Phys. Rev. A 81 052334
[45]	Ghose S, Debnath S, Sinclair N, Kabra A and Stock R 2010 J. Phys. A 43 445301
[46]	Zhao J Q, Cao L Z, Lu H X and Wang X Q 2013 Acta Phys. Sin. 62 120301 (in Chinese)
[47]	Deng F G, Long G L and Liu X S 2003 Phys. Rev. A 68 042317
[48]	Gao T, Yan F L and Wang Z X 2004 J. Phys. A 37 3211
[49]	Gao T 2004 Commun. Theor. Phys. 42 223
[50]	Li X H, Duan X J, Sheng Y B, Zhou H Y and Deng F G 2009 Chin. Phys. B 18 3710
[51]	Ding D and Yan F L 2013 Phys. Lett. A 377 1088
[52]	Liu Y, Chen T Y, Wang L J, Liang H, Shentu G L, Wang J, Cui K, Yin H L, Liu N L, Li L, Ma X F, Pelc J S, Fejer M M, Peng C Z, Zhang Q and Pan J W 2013 Phys. Rev. Lett. 111 130502

Quantum nonlocality of generic family of four-qubit entangled pure states

Quantum nonlocality of generic family of four-qubit entangled pure states

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 52

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Xiao-Qiang Su(苏晓强), Zong-Ju Xu(许宗菊), and You-Quan Zhao(赵有权). Entanglement and thermalization in the extended Bose-Hubbard model after a quantum quench: A correlation analysis[J]. 中国物理B, 2023, 32(2): 20506-020506.
[2]	Yuan-Yuan Liu(刘元元), Zhi-Ming Zhang(张智明), Jun-Hao Liu(刘军浩), Jin-Dong Wang(王金东), and Ya-Fei Yu(於亚飞). Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system[J]. 中国物理B, 2022, 31(9): 94203-094203.
[3]	Kai-Qian Huang(黄恺芊), Wei-Lin Li(李蔚琳), Wen-Lei Zhao(赵文垒), and Zhi Li(李志). Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators[J]. 中国物理B, 2022, 31(9): 90301-090301.
[4]	Xiao-Long Gong(龚小龙), Shuo Cao(曹硕), Yue Fang(方越), and Tong-Hua Liu(刘统华). Relativistic motion on Gaussian quantum steering for two-mode localized Gaussian states[J]. 中国物理B, 2022, 31(5): 50402-050402.
[5]	Qilin Zheng(郑骑林), Jiacheng Liu(刘嘉成), Chao Wu(吴超), Shichuan Xue(薛诗川), Pingyu Zhu(朱枰谕), Yang Wang(王洋), Xinyao Yu(于馨瑶), Miaomiao Yu(余苗苗), Mingtang Deng(邓明堂), Junjie Wu(吴俊杰), and Ping Xu(徐平). Bright 547-dimensional Hilbert-space entangled resource in 28-pair modes biphoton frequency comb from a reconfigurable silicon microring resonator[J]. 中国物理B, 2022, 31(2): 24206-024206.
[6]	M Bagheri Harouni. Influences of spin-orbit interaction on quantum speed limit and entanglement of spin qubits in coupled quantum dots[J]. 中国物理B, 2021, 30(9): 90301-090301.
[7]	Bao-Min Li(李保民), Ming-Liang Hu(胡明亮), and Heng Fan(范桁). Nonlocal advantage of quantum coherence and entanglement of two spins under intrinsic decoherence[J]. 中国物理B, 2021, 30(7): 70307-070307.
[8]	Xin-Feng Jin(金鑫锋), Li-Zhen Jiang(蒋丽珍), and Xiao-Yu Chen(陈小余). Entanglement properties of GHZ and W superposition state and its decayed states[J]. 中国物理B, 2021, 30(6): 60301-060301.
[9]	杜少将, 彭勇刚, 冯海冉, 韩峰, 杨连武, 郑雨军. Reversion of weak-measured quantum entanglement state[J]. 中国物理B, 2020, 29(7): 74202-074202.
[10]	Sare Golkar, Mohammad Kazem Tavassoly, Alireza Nourmandipour. Qubit movement-assisted entanglement swapping[J]. 中国物理B, 2020, 29(5): 50304-050304.
[11]	刘堂昆, 刘飞, 单传家, 刘继兵. Geometrical quantum discord and negativity of two separable and mixed qubits[J]. 中国物理B, 2019, 28(9): 90304-090304.
[12]	李志远. Atom interferometers with weak-measurement path detectors and their quantum mechanical analysis[J]. 中国物理B, 2019, 28(6): 60301-060301.
[13]	刘堂昆, 陶宇, 单传家, 刘继兵. Entropy of field interacting with two two-qubit atoms[J]. 中国物理B, 2018, 27(9): 90303-090303.
[14]	张玉宝, 刘军浩, 於亚飞, 张智明. Entangling two oscillating mirrors in an optomechanical system via a flying atom[J]. 中国物理B, 2018, 27(7): 74209-074209.
[15]	刘婷婷, 胡亚运, 赵静, 钟鸣, 童培庆. The entanglement of deterministic aperiodic quantum walks[J]. 中国物理B, 2018, 27(12): 120305-120305.