A protocol to transform Svetlichny's genuine multipartite correlations into standard isotropic form

doi:10.1088/1674-1056/21/7/070307

中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70307-070307.doi: 10.1088/1674-1056/21/7/070307

A protocol to transform Svetlichny's genuine multipartite correlations into standard isotropic form

向阳, 任喜军

School of Physics and Electronics, Henan University, Kaifeng 475001, China

收稿日期:2012-03-19 修回日期:2012-04-09 出版日期:2012-06-01 发布日期:2012-06-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11005031 and 11047174).

A protocol to transform Svetlichny's genuine multipartite correlations into standard isotropic form

Xiang Yang(向阳)^† and Ren Xi-Jun(任喜军)

School of Physics and Electronics, Henan University, Kaifeng 475001, China

Received:2012-03-19 Revised:2012-04-09 Online:2012-06-01 Published:2012-06-01
Contact: Xiang Yang E-mail:njuxy@sohu.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11005031 and 11047174).

摘要/Abstract

摘要： The standard isotropic correlations are widely used in the research of no-locality of quantum physics. We prove that any multipartite no-signaling correlation can be transformed into standard isotropic form through a randomization procedure which do not change Svetlichny's genuine multipartite correlation. For the tripartite correlations, every part with two-input and two-outcome, we explicitly give the protocol and the proof of its validity. We then generalize the protocol to deal with the case of N-partite.

关键词: Svetlichny's genuine multipartite correlation, isotropic form

Abstract: The standard isotropic correlations are widely used in the research of no-locality of quantum physics. We prove that any multipartite no-signaling correlation can be transformed into standard isotropic form through a randomization procedure which do not change Svetlichny's genuine multipartite correlation. For the tripartite correlations, every part with two-input and two-outcome, we explicitly give the protocol and the proof of its validity. We then generalize the protocol to deal with the case of N-partite.

Key words: Svetlichny's genuine multipartite correlation, isotropic form

中图分类号: (Entanglement and quantum nonlocality)

03.65.Ud

03.67.Mn (Entanglement measures, witnesses, and other characterizations)

向阳, 任喜军 . A protocol to transform Svetlichny's genuine multipartite correlations into standard isotropic form[J]. 中国物理B, 2012, 21(7): 70307-070307.

Xiang Yang(向阳) and Ren Xi-Jun(任喜军) . A protocol to transform Svetlichny's genuine multipartite correlations into standard isotropic form[J]. Chin. Phys. B, 2012, 21(7): 70307-070307.

参考文献 35

[1]	Bell J S 1964 Physics 1 195
[2]	Clauser J F, Horne M A, Shimony A and Holt R A 1969 Phys. Rev. Lett. 23 880
[3]	Clauser J F, Horne M A, Shimony A and Holt R A 1970 Phys. Rev. Lett. 24 549(E)
[4]	Cirel'son B S 1980 Lett. Math. Phys. 4 93
[5]	Popescu S and Rohrlich D 1994 Found. Phys. 24 379
[6]	Barrett J, Linden N, Massar S, Pironio S, Popescu S and Roberts D 2005 Phy. Rev. A 71 022101
[7]	Masanes L, Acin A and Gisin N 2006 Phys. Rev. A 73 012112
[8]	Barrett J 2007 Phys. Rev. A 75 032304
[9]	Barnum H, Barrett J, Leifer M and Wilce A 2007 Phys. Rev. Lett. 99 240501
[10]	Li J J and Wang Z X 2010 Chin. Phys. B 19 100310
[11]	Scarani V, Gisin N, Brunner N, Masanes L, Pino S and Acin A 2006 Phys. Rev. A 74 042339
[12]	Barrett J, Hardy L and Kent A 2005 Phys. Rev. Lett. 95 010503
[13]	Acín A, Gisin N and Masanes L 2006 Phys. Rev. Lett. 97 120405
[14]	Yang Y G and Wen Q Y 2007 Chin. Phys. B 16 2215
[15]	Chen M J and Liu X 2011 Chin. Phys. B 20 100305
[16]	van Dam W 2005 arXiv: quant-ph/0501159
[17]	Brassard G, Buhrman H, Linden N, M閠hot A A, Tapp A and Unger F 2006 Phys. Rev. Lett. 96 250401
[18]	Linden N, Popescu S, Short A J and Winter A 2007 Phys. Rev. Lett. 99 180502
[19]	Brunner N and Skrzypczyk P 2009 Phys. Rev. Lett. 102 160403
[20]	Barnum H, Beigi S, Boixo S, Elliott M B and Wehner S 2010 Phys. Rev. Lett. 104 140401
[21]	Acín A, Augusiak R, Cavalcanti D, Hadley C, Korbizc J K, Lewenstein M, Masanes L and Piani M 2010 Phys. Rev. Lett. 104 140404
[22]	Pawlowski M, Paterek T, Kaszlikowski D, Scarani V, Winter A and Żukowski M 2009 Nature 461 1101
[23]	Allcock J, Brunner N, Pawlowski M and Scarani V 2009 Phys. Rev. A 80 040103(R)
[24]	Cavalcanti D, Cavalcanti D, Salles A and Scarani V 2010 Nat. Comm. 1 136
[25]	Xiang Y and Ren W 2011 Quant. Inf. Comput. 11 0948
[26]	Pironio S, Bancal J D and Scarani V 2011 J. Phys. A: Math. Theor. 44 065303
[27]	Svetlichny G 1987 Phys. Rev. D 35 3066
[28]	Seevinck M and Svetlichny G 2002 Phys. Rev. Lett. 89 060401
[29]	Mitchell P, Popescu S and Roberts D 2004 Phys. Rev. A 70 060101
[30]	Deng D L, Zhou Z S and Chen J L 2009 Phys. Rev. A 80 022109
[31]	Bancal J D, Brunner N, Gisin N and Liang Y C 2011 Phys. Rev. Lett. 106 020405
[32]	Chen J L, Deng D L, Su H Y, Wu C F and Oh C H 2011 Phys. Rev. A 83 022316
[33]	Deng D L, Gu S J and Chen J L 2010 Ann. Phys. 325 367
[34]	Aolita L, Gallego R, Cabello A and Acín A 2012 Phys. Rev. Lett. 108 100401
[35]	Masanes L, Acín A and Gisin N 2006 Phys. Rev. A 73 012112

A protocol to transform Svetlichny's genuine multipartite correlations into standard isotropic form

A protocol to transform Svetlichny's genuine multipartite correlations into standard isotropic form

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 35

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Qi Sun(孙琪), Tao Li(李陶), Zhi-Xiang Jin(靳志祥), and Deng-Feng Liang(梁登峰). Unified entropy entanglement with tighter constraints on multipartite systems[J]. 中国物理B, 2023, 32(3): 30304-030304.
[2]	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.
[3]	Qing-Yun Zhou(周晴云), Xiao-Gang Fan(范小刚), Fa Zhao(赵发), Dong Wang(王栋), and Liu Ye(叶柳). Transformation relation between coherence and entanglement for two-qubit states[J]. 中国物理B, 2023, 32(1): 10304-010304.
[4]	Jia-Wei Ying(应佳伟), Lan Zhou(周澜), Wei Zhong(钟伟), and Yu-Bo Sheng(盛宇波). Measurement-device-independent one-step quantum secure direct communication[J]. 中国物理B, 2022, 31(12): 120303-120303.
[5]	Ye-Qi Zhang(张业奇), Xiao-Ting Ding(丁潇婷), Jiao Sun(孙娇), and Tian-Hu Wang(王天虎). Quantum steerability of two qubits mediated by one-dimensional plasmonic waveguides[J]. 中国物理B, 2022, 31(12): 120305-120305.
[6]	Ying-Yue Yang(杨颖玥), Li-Juan Li(李丽娟), Liu Ye(叶柳), and Dong Wang(王栋). Quantum correlation and entropic uncertainty in a quantum-dot system[J]. 中国物理B, 2022, 31(10): 100303-100303.
[7]	Xing-Xing Ju(居星星), Wei Zhong(钟伟), Yu-Bo Sheng(盛宇波), and Lan Zhou(周澜). Measurement-device-independent quantum secret sharing with hyper-encoding[J]. 中国物理B, 2022, 31(10): 100302-100302.
[8]	Huan Yang(杨欢), Ling-Ling Xing(邢玲玲), Zhi-Yong Ding(丁智勇), Gang Zhang(张刚), and Liu Ye(叶柳). Steering quantum nonlocalities of quantum dot system suffering from decoherence[J]. 中国物理B, 2022, 31(9): 90302-090302.
[9]	Hengji Li(李恒吉), Jian Li(李剑), and Xiubo Chen(陈秀波). Probabilistic quantum teleportation of shared quantum secret[J]. 中国物理B, 2022, 31(9): 90303-090303.
[10]	Zhan-Yun Wang(王展云), Feng-Lin Wu(吴风霖), Zhen-Yu Peng(彭振宇), and Si-Yuan Liu(刘思远). Robustness of two-qubit and three-qubit states in correlated quantum channels[J]. 中国物理B, 2022, 31(7): 70302-070302.
[11]	I Reena, H S Karthik, J Prabhu Tej, Sudha, A R Usha Devi, and A K Rajagopal. Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems[J]. 中国物理B, 2022, 31(6): 60301-060301.
[12]	Bichen Che(车碧琛), Zhao Dou(窦钊), Xiubo Chen(陈秀波), Yu Yang(杨榆), Jian Li(李剑), and Yixian Yang(杨义先). Constructing the three-qudit unextendible product bases with strong nonlocality[J]. 中国物理B, 2022, 31(6): 60302-060302.
[13]	Xiao-Fang Liu(刘晓芳), Dong-Fen Li(李冬芬), Yun-Dan Zheng(郑云丹), Xiao-Long Yang(杨小龙), Jie Zhou(周杰), Yu-Qiao Tan(谭玉乔), and Ming-Zhe Liu(刘明哲). Experimental realization of quantum controlled teleportation of arbitrary two-qubit state via a five-qubit entangled state[J]. 中国物理B, 2022, 31(5): 50301-050301.
[14]	Yong-Ting Liu(刘永婷), Yi-Ming Wu(吴一鸣), and Fang-Fang Du(杜芳芳). Self-error-rejecting multipartite entanglement purification for electron systems assisted by quantum-dot spins in optical microcavities[J]. 中国物理B, 2022, 31(5): 50303-050303.
[15]	Xue-Yun Bai(白雪云) and Su-Ying Zhang(张素英). Protecting geometric quantum discord via partially collapsing measurements of two qubits in multiple bosonic reservoirs[J]. 中国物理B, 2022, 31(4): 40308-040308.