| GENERAL |
|
|
|
|
Separability Criterion for Bipartite States and Its Generalization to Multipartite Systems |
| HUANG Jie-Hui1**, HU Li-Yun1, WANG Lei2, ZHU Shi-Yao3 |
1College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022
2College of Physics, Jilin University, Changchun 130021
3Beijing Computational Science Research Center, Beijing 100084
|
|
| Cite this article: |
|
HUANG Jie-Hui, HU Li-Yun, WANG Lei et al 2014 Chin. Phys. Lett. 31 040303 |
|
|
|
|
Abstract A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. All the symmetric operators, represented by a symmetric matrix with only two nonzero elements, and their arbitrary linear combinations are found to be entanglement witnesses. By using these symmetric operators, Wootters' separability criterion for two-qubit states can be generalized to bipartite and multipartite systems in arbitrary dimensions.
|
|
|
Received: 27 November 2013
Published: 25 March 2014
|
|
| PACS: |
03.67.Mn
|
(Entanglement measures, witnesses, and other characterizations)
|
| |
03.65.Fd
|
(Algebraic methods)
|
|
|
|
|
|
[1] Einstein A, Podolsky B and Rosen N 1935 Phys. Rev. 47 777
[2] Schr?dinger E and Born M 1935 Math. Proc. Cambridge Philos. Soc. 31 555
[3] Schr?dinger E and Dirac P A M 1936 Math. Proc. Cambridge Philos. Soc. 32 446
[4] Werner R F 1989 Phys. Rev. A 40 4277
[5] Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A and Wootters W K 1996 Phys. Rev. Lett. 76 722
[6] Bennett C H, DiVincenzo D P, Smolin J A and Wootters W K 1996 Phys. Rev. A 54 3824
[7] Vedral V and Plenio M B 1998 Phys. Rev. A 57 1619
[8] Terhal B M and Horodecki P 2000 Phys. Rev. A 61 040301
[9] Sanpera A, Bru? D and Lewenstein M 2001 Phys. Rev. A 63 050301
[10] Hill S and Wootters W K 1997 Phys. Rev. Lett. 78 5022
[11] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[12] ?yczkowski K, Horodecki P, Sanpera A and Lewenstein M 1998 Phys. Rev. A 58 883
[13] Vidal G and Werner R F 2002 Phys. Rev. A 65 032314
[14] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[15] Coffman V, Kundu J and Wootters W K 2000 Phys. Rev. A 61 052306
[16] Meyer D A and Wallach N R 2001 arXiv:quant-ph/0108104
[17] Eisert J and Briegel H J 2001 Phys. Rev. A 64 022306
[18] Barnum H and Linden N 2001 J. Phys. A 34 6787
[19] Amico L, Fazio R, Osterloh A and Vedral V 2008 Rev. Mod. Phys. 80 517
[20] Peres A 1996 Phys. Rev. Lett. 77 1413
[21] Horodecki M, Horodecki P and Horodecki R 1996 Phys. Lett. A 223 1
[22] Uhlmann A 2000 Phys. Rev. A 62 032307
[23] Wong A and Christensen N 2001 Phys. Rev. A 63 044301
[24] Mintert F, Ku? M and Buchleitner A 2004 Phys. Rev. Lett. 92 167902
[25] Rungta P, Buzek V, Caves C M, Hillery M and Milburn G J 2001 Phys. Rev. A 64 042315
[26] Mintert F, Ku? M and Buchleitner A 2005 Phys. Rev. Lett. 95 260502
[27] Akhtarshenas S J 2005 J. Phys. A 38 6777
[28] Chen Z H, Ma Z H, Gühne O and Severini S 2012 Phys. Rev. Lett. 109 200503
[29] Terhal B M 2000 Phys. Lett. A 271 319
[30] Lewenstein M, Kraus B, Cirac J I and Horodecki P 2000 Phys. Rev. A 62 052310
[31] Terhal B M 2001 Linear Algebr. Appl. 323 61
[32] Brand ao F G S L 2005 Phys. Rev. A 72 022310
[33] Tóth G and Gühne O 2005 Phys. Rev. Lett. 94 060501
[34] Horn R A and Johnson C R 1985 Matrix Analysis (New York: Cambridge University Press) p 205
[35] Vedral V, Plenio M B, Rippin M A and Knight P L 1997 Phys. Rev. Lett. 78 2275
[36] Yu C S and Song H S 2006 Phys. Rev. A 73 022325 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
