Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(9): 090315    DOI: 10.1088/1674-1056/19/9/090315
GENERAL Prev   Next  

Concurrence, tangle and fully entangled fraction

Li Ming(李明)a), Fei Shao-Ming(费少明)b), and Li-Jost Xianqing(李先清)c)
a College of Mathematics and Computational Science, China University of Petroleum, Dongying 257061, China; b Department of Mathematics, Capital Normal University, Beijing 100037, China; c Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
Abstract  We show that although we cannot distil a singlet from many pairs of bound entangled states, the concurrence and the tangle of two entangled quantum states are always strictly larger than those of one of them, even both entangled quantum states are bound entangled. We present a relation between the concurrence and the fidelity of optimal teleportation. We also give new upper and lower bounds for concurrence and tangle.
Keywords:  concurrence      entanglement      teleportation  
Received:  30 December 2009      Revised:  04 May 2010      Accepted manuscript online: 
PACS:  0367  
  0220H  
  0365W  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10774088, 10675086, 10875081, and 10871227), and the National Basic Research Program of China(Grant No. 2004CB318000).

Cite this article: 

Li Ming(李明), Fei Shao-Ming(费少明), and Li-Jost Xianqing(李先清) Concurrence, tangle and fully entangled fraction 2010 Chin. Phys. B 19 090315

[1] Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[2] Horodecki M, Horodecki P and Horodecki R 1998 Phys. Rev. Lett. 80 5239
[3] Horodecki M, Horodecki P and Horodecki R 1999 Phys. Rev. A 60 1888
[4] Horodecki P, Horodecki M and Horodecki R 1999 Phys. Rev. Lett. 82 1056
[5] Masanes L 2006 Phys. Rev. Lett. 96 150501
[6] Bennett C H, DiVincenzo D P and Smolin J A 1996 Phys. Rev. A 54 3824
[7] Uhlmann A 2000 Phys. Rev. A 62 032307
[8] Rungta P, Buddotzek V and Caves C M 2001 Phys. Rev. A 64 042315
[9] Albeverio S and Fei S M 2001 J. Opt. B: Quantum Semiclass. Opt. 3 223
[10] Aolita L and Mintert F 2006 Phys. Rev. Lett. 97 050501
[11] Carvalho A R R, Mintert F and Buchleitner A 2004 Phys. Rev. Lett. 93 230501
[12] Chen K, Albeverio S and Fei S M 2005 Phys. Rev. Lett. 95 040504
[13] Gao X H, Fei S M and Wu K 2007 Phys. Rev. A 74 050303(R)
[14] de Vicente J I 2007 Phys. Rev. A 75 052320
[15] de Vicente J I 2008 J. Phys. A: Math. Theor. 41 065309
[16] Zhang C J, Gong Y X, Zhang Y S and Guo G C 2008 Phys. Rev. A 78 042308
[17] Chen K, Albeverio S and Fei S M 2005 Phys. Rev. Lett. 95 210501
[18] Vidal G, Jonathan D and Nielsen M A 2000 Phys. Rev. A 62 012304
[19] Coffman V, Kundu J and Wootters W K 2000 Phys. Rev. A 61 052306
[20] Rungta P and Caves C M 2003 Phys. Rev. A 67 012307
[21] Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A and Wooters W K 1993 Phys. Rev. Lett. 70 1895
[22] Ren J G, Yang B, Yi Z H, Zhou F, Chen K, Peng C Z and Pan J W 2009 Chin. Phys. B 18 3605
[23] Ai L Y, Du G, Zhu S L and Zhang Z M 2009 Chin. Phys. Lett. bf26 014210
[24] Sun Y, Man Z X and Xia Y J 2009 Chin. Phys. Lett. bf26 020306
[25] Grondalski J, Etlinger D M and James D F V 2002 Phys. Lett. A 300 573 %1999 Phys. Rev. A 60 1888
[26] Albeverio S, Fei S M and Yang W L 2002 Phys. Rev. A 66 012301
[27] Yu C S, Yi X X and Song H S 2008 Phys. Rev. A 78 062330
[28] Zhang C J, Zhang Y S, Zhang S and Guo G C 2007 Phys. Rev. A 76 012334
[29] Li M, Fei S M and Wang Z X 2008 J. Phys. A(FTC) 41 202002
[30] Cai J M, Zhou Z W, Zhang S and Guo G C 2007 Phys. Rev. A 75 052324
[31] Mintert F and Buchleitner A 2007 Phys. Rev. Lett. 98 140505
[32] Aolita L, Buchleitner A and Mintert F 2008 Phys. Rev. A 78 022308
[33] Ruskai M B 2007 Rep. Math. Phys. 60 1
[34] Nielsen M and Petz D 2005 Quantum Inf. Comput. 5 507
[1] Unified entropy entanglement with tighter constraints on multipartite systems
Qi Sun(孙琪), Tao Li(李陶), Zhi-Xiang Jin(靳志祥), and Deng-Feng Liang(梁登峰). Chin. Phys. B, 2023, 32(3): 030304.
[2] Entanglement and thermalization in the extended Bose-Hubbard model after a quantum quench: A correlation analysis
Xiao-Qiang Su(苏晓强), Zong-Ju Xu(许宗菊), and You-Quan Zhao(赵有权). Chin. Phys. B, 2023, 32(2): 020506.
[3] Improving the teleportation of quantum Fisher information under non-Markovian environment
Yan-Ling Li(李艳玲), Yi-Bo Zeng(曾艺博), Lin Yao(姚林), and Xing Xiao(肖兴). Chin. Phys. B, 2023, 32(1): 010303.
[4] Transformation relation between coherence and entanglement for two-qubit states
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). Chin. Phys. B, 2023, 32(1): 010304.
[5] Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators
Kai-Qian Huang(黄恺芊), Wei-Lin Li(李蔚琳), Wen-Lei Zhao(赵文垒), and Zhi Li(李志). Chin. Phys. B, 2022, 31(9): 090301.
[6] Probabilistic quantum teleportation of shared quantum secret
Hengji Li(李恒吉), Jian Li(李剑), and Xiubo Chen(陈秀波). Chin. Phys. B, 2022, 31(9): 090303.
[7] Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system
Yuan-Yuan Liu(刘元元), Zhi-Ming Zhang(张智明), Jun-Hao Liu(刘军浩), Jin-Dong Wang(王金东), and Ya-Fei Yu(於亚飞). Chin. Phys. B, 2022, 31(9): 094203.
[8] Direct measurement of two-qubit phononic entangled states via optomechanical interactions
A-Peng Liu(刘阿鹏), Liu-Yong Cheng(程留永), Qi Guo(郭奇), Shi-Lei Su(苏石磊), Hong-Fu Wang(王洪福), and Shou Zhang(张寿). Chin. Phys. B, 2022, 31(8): 080307.
[9] Purification in entanglement distribution with deep quantum neural network
Jin Xu(徐瑾), Xiaoguang Chen(陈晓光), Rong Zhang(张蓉), and Hanwei Xiao(肖晗微). Chin. Phys. B, 2022, 31(8): 080304.
[10] Robustness of two-qubit and three-qubit states in correlated quantum channels
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). Chin. Phys. B, 2022, 31(7): 070302.
[11] Experimental realization of quantum controlled teleportation of arbitrary two-qubit state via a five-qubit entangled state
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). Chin. Phys. B, 2022, 31(5): 050301.
[12] Self-error-rejecting multipartite entanglement purification for electron systems assisted by quantum-dot spins in optical microcavities
Yong-Ting Liu(刘永婷), Yi-Ming Wu(吴一鸣), and Fang-Fang Du(杜芳芳). Chin. Phys. B, 2022, 31(5): 050303.
[13] Effects of colored noise on the dynamics of quantum entanglement of a one-parameter qubit—qutrit system
Odette Melachio Tiokang, Fridolin Nya Tchangnwa, Jaures Diffo Tchinda,Arthur Tsamouo Tsokeng, and Martin Tchoffo. Chin. Phys. B, 2022, 31(5): 050306.
[14] Probabilistic resumable quantum teleportation in high dimensions
Xiang Chen(陈想), Jin-Hua Zhang(张晋华), and Fu-Lin Zhang(张福林). Chin. Phys. B, 2022, 31(3): 030302.
[15] Tetrapartite entanglement measures of generalized GHZ state in the noninertial frames
Qian Dong(董茜), R. Santana Carrillo, Guo-Hua Sun(孙国华), and Shi-Hai Dong(董世海). Chin. Phys. B, 2022, 31(3): 030303.
No Suggested Reading articles found!