Relative entropy of entanglement of two-qubit 'X' states

doi:10.1088/1674-1056/19/11/110307

中国物理B ›› 2010, Vol. 19 ›› Issue (11): 110307-110312.doi: 10.1088/1674-1056/19/11/110307

Relative entropy of entanglement of two-qubit 'X' states

黄接辉, 刘念华, 刘江涛, 于天宝, 何弦

Department of Physics, Nanchang University, Nanchang 330031, China

收稿日期:2010-03-24 修回日期:2010-06-03 出版日期:2010-11-15 发布日期:2010-11-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10804042), and also supported by the Scientific Research Foundation of the Education Department of Jiangxi Province, China (Project No. GJJ09440).

Relative entropy of entanglement of two-qubit 'X' states

Huang Jie-Hui(黄接辉)^†ger, Liu Nian-Hua(刘念华), Liu Jiang-Tao(刘江涛), Yu Tian-Bao(于天宝), and He Xian(何弦)

Department of Physics, Nanchang University, Nanchang 330031, China

Received:2010-03-24 Revised:2010-06-03 Online:2010-11-15 Published:2010-11-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10804042), and also supported by the Scientific Research Foundation of the Education Department of Jiangxi Province, China (Project No. GJJ09440).

摘要/Abstract

摘要： Two closest single-qubit states could be diagonalised by the same unitary matrix, which helps to find the relative entropy of entanglement of a two-qubit `X' state. We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit `X' state. This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states, such as pure states, Werner states, and so on.

Abstract: Two closest single-qubit states could be diagonalised by the same unitary matrix, which helps to find the relative entropy of entanglement of a two-qubit 'X' state. We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit 'X' state. This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states, such as pure states, Werner states, and so on.

Key words: relative entropy of entanglement, two-qubit state

中图分类号: (Algebraic methods)

03.65.Fd

03.65.Ud (Entanglement and quantum nonlocality) 03.67.Lx (Quantum computation architectures and implementations) 03.67.Mn (Entanglement measures, witnesses, and other characterizations) 05.70.Ce (Thermodynamic functions and equations of state)

黄接辉, 刘念华, 刘江涛, 于天宝, 何弦. Relative entropy of entanglement of two-qubit 'X' states[J]. 中国物理B, 2010, 19(11): 110307-110312.

Huang Jie-Hui(黄接辉), Liu Nian-Hua(刘念华), Liu Jiang-Tao(刘江涛), Yu Tian-Bao(于天宝), and He Xian(何弦). Relative entropy of entanglement of two-qubit 'X' states[J]. Chin. Phys. B, 2010, 19(11): 110307-110312.

参考文献 26

[1]	Bennett C H, DiVincenzo D P, Smolin J and Wootters W K 1996 Phys. Rev. A 54 3824
[2]	Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A and Wootters W K 1996 Phys. Rev. Lett. 76 722
[3]	Vedral V, Plenio M B, Rippin M A and Knight P L 1997 Phys. Rev. Lett. 78 2275
[4]	Vedral V and Plenio M B 1998 Phys. Rev. A 57 1619
[5]	Wootters W K 1998 Phys. Rev. Lett. 80 2245
[6]	Vidal G and Werner R F 2002 Phys. Rev. A 65 032314
[7]	Christandl M and Winter A 2004 J. Math. Phys. 45 829
[8]	Uhlmann A 2000 Phys. Rev. A 62 032307
[9]	Rungta P, Buvzek V, Caves C M, Hillery M and Milburn G J 2001 Phys. Rev. A 64 042315
[10]	Coffman V, Kundu J and Wootters W K 2000 Phys. Rev. A 61 052306
[11]	Qin M 2010 Acta Phys. Sin. 59 2212 (in Chinese)
	Ma P C and Zhan Y B 2008 Chin. Phys. B 17 445
[12]	Verstraete F, Audenaert K and De Moor B 2001 Phys. Rev. A 64 012316
[13]	Verstraete F, Audenaert K M R, Dehaene J and De Moor B 2001 J. Phys. A 34 10327
[14]	Verstraete F, Dehaene J and De Moor B 2002 J. Mod. Opt. 49 1277
[15]	Audenaert K M R, De Moor B, Vollbrecht K G H and Werner R F 2002 Phys. Rev. A 66 032310
[16]	Chen X Y, Meng L M, Jiang L Z and Li X J 2005 Chin. Phys. Lett. 22 2755
[17]	Rehacek J, Hradil Z and Jezek M 2001 Phys. Rev. A 63 040303
[18]	Rehacek J and hradil Z 2003 Phys. Rev. Lett. 90 127904
[19]	Ishizaka S 2002 J. Phys. A 35 8075
[20]	Ishizaka S 2003 Phys. Rev. A 67 060301(R)
[21]	Ishizaka S 2004 Phys. Rev. A 69 020301(R)
[22]	Miranowicz A and Ishizaka S 2008 Phys. Rev. A 78 032310
[23]	Peres A 1996 Phys. Rev. Lett. 77 1413
[24]	Horodecki M, Horodecki P and Horodecki R 1996 Phys. Lett. A 223 1
[25]	Werner R F 1989 Phys. Rev. A 40 4277
[26]	Vollbrecht K G H and Werner R F 2002 Phys. Rev. A 64 062307 endfootnotesize

Relative entropy of entanglement of two-qubit 'X' states

Relative entropy of entanglement of two-qubit 'X' states

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