A note on local unitary equivalence of isotropic-like states

doi:10.1088/1674-1056/24/12/120305

Abstract We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition.

Keywords: mixed state local unitary equivalence local unitary similar equivalence

Received: 17 July 2015
Revised: 20 August 2015
Accepted manuscript online:

PACS:	03.67.-a	(Quantum information)
	02.20.Hj	(Classical groups)
	03.65.-w	(Quantum mechanics)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11401032, 61473325, 11501153, 11105226, 11275131, and 11401106), the Fundamental Research Funds for the Central Universities, China (Grant Nos. 15CX08011A and 24720122013), the Natural Science Foundation of Hainan Province, China (Grant Nos. 20151005 and 20151010), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

Corresponding Authors: Zhang Ting-Gui, Zhao Ming-Jing
E-mail: tinggui333@163.com;zhaomingjingde@126.com

Cite this article:

Zhang Ting-Gui (张廷桂), Hua Bo-Bo (华波波), Li Ming (李明), Zhao Ming-Jing (赵明镜), Yang Hong (杨红) A note on local unitary equivalence of isotropic-like states 2015 Chin. Phys. B 24 120305

[1]	Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[2]	Dür W, Vidal G and Cirac J I 2000 Phys. Rev. A 62 062314
[3]	Li Y J and Liu J M 2014 Acta Phys. Sin. 63 200302 (in Chinese)
[4]	Mazhar A 2014 Chin. Phys. B 23 120307
[5]	Wang Z X and Wang B B 2014 Chin. Phys. B 23 070305
[6]	Zhu H J and Zhang G F 2014 Chin. Phys. B 23 0120306
[7]	Grassl M, Rötteler M and Beth T 1998 Phys. Rev. A 58 1833
[8]	Makhlin Y 2002 Quantum Inforn. Process. 1 243
[9]	Linden N, Popescu S and Sudbery A 1999 Phys. Rev. Lett. 83 243
[10]	Linden N and Popescu S 1998 Physica 46 567
[11]	Albeverio S, Fei S M, Parashar P and Yang W L 2003 Phys. Rev. A 68 010303
[12]	Albeverio S, Fei S M and Goswami D 2005 Phys. Lett. A 340 37
[13]	Sun B Z, Fei S M, Li-Jost X and Wang Z X 2006 J. Phys. A: Math. Gen. 39 L43
[14]	Albeverio S, Cattaneo L, Fei S M and Wang X H 2005 Int. J. Quantum Inform. 3 603
[15]	Zhang T G, Jing N, Li-Jost X, Zhao M J and Fei S M 2013 Eur. Phys. J. D 67 175
[16]	Kraus B 2010 Phys. Rev. Lett. 104 020504
[17]	Kraus B 2010 Phys. Rev. A 82 032121
[18]	Liu B, Li J L, Li X and Qiao C F 2012 Phys. Rev. Lett. 108 050501
[19]	Zhou C, Zhang T, Fei S M, Jing N and Li-Jost X 2012 Phys. Rev. A 86 010303
[20]	Zhang T G, Zhao M J, Li-Jost X and Fei S M 2013 Int. J. Theor. Phys. 52 3020
[21]	Zhang T G, Zhao M J, Li M, Fei S M and Li-Jost X 2013 Phys. Rev. A 88 042304
[22]	Li M, Zhang T G, Fei S M, Li-Jost X and Jing N 2014 Phys. Rev. A 89 062325
[23]	Horodecki M and Horodecki P 1999 Phys. Rev. A 59 4206
[24]	Werner R F 1989 Phys. Rev. A 40 4277
[25]	Horodecki M, Horodecki P and Horodecki R 1996 Phys. Lett. A 223 1
[26]	Lathaumer L D, Moor B D and Vandewalle J 2000 SIAM. J. Matrix Anal. Appl. 21 1253
[27]	Shapiro H 1991 Linear Algebra Appl. 147 101
[28]	Specht W 1940 Deutsch. Math.-Verein 50 19
[29]	Wiegmann N 1962 J. Austral. Math. Soc. 2 122

[1]	Boundary states for entanglement robustness under dephasing and bit flip channels Hong-Mei Li(李红梅), Miao-Di Guo(郭苗迪), Rui Zhang(张锐), Xue-Mei Su(苏雪梅). Chin. Phys. B, 2019, 28(10): 100302.
[2]	Experimentally testing Hardy's theorem on nonlocality with entangled mixed states Dai-He Fan(樊代和), Mao-Chun Dai(戴茂春), Wei-Jie Guo(郭伟杰), Lian-Fu Wei(韦联福). Chin. Phys. B, 2017, 26(4): 040302.
[3]	Fidelity between Gaussian mixed states with quantum state quadrature variances Hai-Long Zhang(张海龙), Chun Zhou(周淳), Jian-Hong Shi(史建红), Wan-Su Bao(鲍皖苏). Chin. Phys. B, 2016, 25(4): 040304.
[4]	A geometric phase for superconducting qubits under the decoherence effect S. Abdel-Khalek, K. Berrada, Mohamed A. El-Sayed, M. Abel-Aty. Chin. Phys. B, 2013, 22(10): 100301.
[5]	Entanglement evolution of three-qubit mixed states in multipartite cavity–reservoir systems Xu Jing-Zhou (许景周), Guo Jin-Bao (郭金宝), Wen Wei (文伟), Bai Yan-Kui (白彦魁), Yan Feng-Li (闫凤利 ). Chin. Phys. B, 2012, 21(8): 080305.
[6]	Entanglement dynamics of a moving multi-photon Jaynes–Cummings model in mixed states Tan Lei(谭磊), Zhang Yu-Qing(张玉青), and Zhu Zhong-Hua(朱中华) . Chin. Phys. B, 2011, 20(7): 070303.
[7]	Separability criteria for multipartite quantum mixed states Zhao Hui (赵慧). Chin. Phys. B, 2005, 14(2): 257-262.
[8]	The study of the valence bond property in a two-different-quantum-dot molecule Wang Li-Min (王立民), Luo Ying (罗莹), Ma Ben-Kun (马本堃). Chin. Phys. B, 2002, 11(2): 150-155.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

A note on local unitary equivalence of isotropic-like states

Cite this article:

Online attention