Separability criteria based on Heisenberg-Weyl representation of density matrices

doi:10.1088/1674-1056/27/3/030302

中国物理B ›› 2018, Vol. 27 ›› Issue (3): 30302-030302.doi: 10.1088/1674-1056/27/3/030302

Separability criteria based on Heisenberg-Weyl representation of density matrices

Jingmei Chang(常景美), Meiyu Cui(崔美钰), Tinggui Zhang(张廷桂), Shao-Ming Fei(费少明)

1 School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China;
2 Hainan Center for Mathematical Research, Hainan Normal University, Haikou 571158, China;
3 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
4 Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany

收稿日期:2017-10-11 修回日期:2017-12-16 出版日期:2018-03-05 发布日期:2018-03-05
通讯作者: Shao-Ming Fei, Tinggui Zhang E-mail:feishm@mail.cnn.edu.cn;tinggui333@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11501153, 11661031, and 11675113) and the National Natural Science Foundation of Hainan Province, China (Grant No. 20161006).

Separability criteria based on Heisenberg-Weyl representation of density matrices

Jingmei Chang(常景美)¹, Meiyu Cui(崔美钰)¹, Tinggui Zhang(张廷桂)^1,2, Shao-Ming Fei(费少明)^3,4

1 School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China;
2 Hainan Center for Mathematical Research, Hainan Normal University, Haikou 571158, China;
3 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
4 Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany

Received:2017-10-11 Revised:2017-12-16 Online:2018-03-05 Published:2018-03-05
Contact: Shao-Ming Fei, Tinggui Zhang E-mail:feishm@mail.cnn.edu.cn;tinggui333@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11501153, 11661031, and 11675113) and the National Natural Science Foundation of Hainan Province, China (Grant No. 20161006).

摘要/Abstract

摘要： Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is shown that this criterion can be better than the previous ones in detecting entanglement. The results are generalized to multipartite quantum states.

关键词: Heisenberg-Weyl observable basis, Bloch representation, separability criterion, multipartite quantum states

Abstract: Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is shown that this criterion can be better than the previous ones in detecting entanglement. The results are generalized to multipartite quantum states.

Key words: Heisenberg-Weyl observable basis, Bloch representation, separability criterion, multipartite quantum states

中图分类号: (Quantum information)

03.67.-a

02.20.Hj (Classical groups) 03.65.-w (Quantum mechanics)

常景美, 崔美钰, 张廷桂, 费少明. Separability criteria based on Heisenberg-Weyl representation of density matrices[J]. 中国物理B, 2018, 27(3): 30302-030302.

Jingmei Chang(常景美), Meiyu Cui(崔美钰), Tinggui Zhang(张廷桂), Shao-Ming Fei(费少明). Separability criteria based on Heisenberg-Weyl representation of density matrices[J]. Chin. Phys. B, 2018, 27(3): 30302-030302.

参考文献 35

[1]	Peres A 1996 Phys. Rev. Lett 77 1413
[2]	Horodecki M, Horodecki P and Horodecki R 1996 Phys. Lett. A 223 1
[3]	Rudolph O 2003 Phys. Rev. A 67 032312
[4]	Chen K and Wu L A 2003 Quantum Inf. Comput. 3 193
[5]	Rudolph O 2005 Quantum Inf. Process. 4 219
[6]	Zhang C J, Zhang Y S, Zhang S and Guo G C 2008 Phys. Rev. A 77 060301
[7]	Aniello P and Lupo C 2008 J. Phys. A:Math. Theor. 41 355303
[8]	Gühne O, Hyllus P, Gittsovich O and Eisert J 2007 Phys. Rev. Lett. 99 130504
[9]	Gittsovich O, Gühne O, Hyllus P and Eisert J 2008 Phys. Rev. A 78 052319
[10]	Gittsovich O, Hyllus P and Gühne O 2010 Phys. Rev. A 82 032306
[11]	Badziag P, Brukner Č, Laskowski W, Paterek T and Żukowski M 2008 Phys. Rev. Lett. 100 140403
[12]	Laskowski W, Markiewicz M, Paterek T and Żukowski M 2011 Phys. Rev A 84 062305
[13]	de Vicente J I 2007 Quantum Inf. Comput. 7 624
[14]	Li M, Wang J, Fei S M and Li-Jost X 2014 Phys. Rev. A 89 022325
[15]	Shen S Q, Wang M Y, Li M and Fei S M 2015 Phys. Rev. A 92 042332
[16]	Lewenstein M, Augusiak R, Chruściński D, Rana S and Samsonowicz J 2016 Phys. Rev. A 93 042335
[17]	Fujikawa K, Oh C H, Umetsu K and Yu S 2016 Annals of Physics 368 248
[18]	Bohnet-Waldraff F, Braun D and Giraud O 2016 Phys. Rev. A 94 042343
[19]	Shen S Q, Yu J, Li M and Fei S M 2016 Sci. Rep. 6 28850
[20]	Werner R F 1989 Phys. Rev. A 40 4277
[21]	Asadian A, Erker P, Huber M and Klöckl C 2016 Phys. Rev. A 94 010301
[22]	Bertlmann R A and Krammer P 2008 J. Phys. A:Math. Theor. 41 235303
[23]	Massar S and Spindel P 2008 Phys. Rev. Lett. 100 190401
[24]	Asadian A, Budroni C, Steinhoff F E S, Rabl P and Gühne O 2015 Phys. Rev. Lett. 114 250403
[25]	Huang X F, Jing N H and Zhang T G 2016 Commun. Theor. Phys. 65 701
[26]	Reinhold A and Krammer P 2008 J. Phys. A:Math. Theor. 41 235303
[27]	Fano U 1983 Rev. Mod. Phys. 55 855
[28]	Horodecki P 1997 Phys. Lett. A 232 333
[29]	de Vicente J I and Huber M 2011 Phys. Rev. A 84 062306
[30]	Hassan A S M and Joag P S 2008 Quantum Inf. Comput. 8 0773
[31]	Chen Z H, Ma Z H, Chen J L and Severini S 2012 Phys. Rev. A 85 062320
[32]	Wootters W K and Fields B D 1989 Ann. Phys. (N.Y.) 191 363
[33]	Bertlmann R A, Durstberger K, Hiesmayr B C and Krammer P 2005 Phys. Rev. A 72 052331
[34]	Chen B, Ma T and Fei S M 2014 Phys. Rev. A 89 064302
[35]	Chen B, Li T and Fei S M 2015 Quant. Inform. Processing 14 2281

Separability criteria based on Heisenberg-Weyl representation of density matrices

Separability criteria based on Heisenberg-Weyl representation of density matrices

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