Symmetric geometric measure and dynamics of quantum discord

doi:10.1088/1674-1056/22/4/040303

中国物理B ›› 2013, Vol. 22 ›› Issue (4): 40303-040303.doi: 10.1088/1674-1056/22/4/040303

Symmetric geometric measure and dynamics of quantum discord

蒋峰建^{a b}, 吕海江^b, 闫新虎^b, 石名俊^a

a Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
b School of Information Engineering, Huangshan University, Huangshan 245041, China

收稿日期:2012-12-21 修回日期:2013-01-25 出版日期:2013-03-01 发布日期:2013-03-01
基金资助:
Project supported by the National Fundamental Research Program of China (Grant Nos. 2007CB925200), the National Natural Science Foundation of China (Grant No. 11275083), and Natural Science Foundation of Anhui Province of China (Grant No. KJ2012B180).

Symmetric geometric measure and dynamics of quantum discord

Jiang Feng-Jian (蒋峰建)^{a b}, Lü Hai-Jiang (吕海江)^b, Yan Xin-Hu (闫新虎)^b, Shi Ming-Jun (石名俊)^a

a Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
b School of Information Engineering, Huangshan University, Huangshan 245041, China

Received:2012-12-21 Revised:2013-01-25 Online:2013-03-01 Published:2013-03-01
Contact: Jiang Feng-Jian, Shi Ming-Jun E-mail:jfjiang@mail.ustc.edu.cn; shmj@ustc.edu.cn
Supported by:
Project supported by the National Fundamental Research Program of China (Grant Nos. 2007CB925200), the National Natural Science Foundation of China (Grant No. 11275083), and Natural Science Foundation of Anhui Province of China (Grant No. KJ2012B180).

摘要/Abstract

摘要： A symmetric measure of quantum correlation based on the Hilbert-Schmidt distance is presented in this paper. For two-qubit states, we simplify considerably the optimization procedure so that numerical evaluation can be performed efficiently. Analytical expressions for the quantum correlation are attained for some special states. We further investigate the dynamics of quantum correlation of the system qubits in the presence of independent dissipative environments. Several nontrivial aspects are demonstrated. We find that the quantum correlation can increase even if the system state is suffering from dissipative noise. Sudden changes occur, even twice, in the time evolution of quantum correlation. There exists a certain correspondence between the evolution of quantum correlation in the systems and that in the environments, and the quantum correlation in the systems will be transferred into the environments completely and asymptotically.

关键词: quantum correlation, geometric measure

Abstract: A symmetric measure of quantum correlation based on the Hilbert-Schmidt distance is presented in this paper. For two-qubit states, we simplify considerably the optimization procedure so that numerical evaluation can be performed efficiently. Analytical expressions for the quantum correlation are attained for some special states. We further investigate the dynamics of quantum correlation of the system qubits in the presence of independent dissipative environments. Several nontrivial aspects are demonstrated. We find that the quantum correlation can increase even if the system state is suffering from dissipative noise. Sudden changes occur, even twice, in the time evolution of quantum correlation. There exists a certain correspondence between the evolution of quantum correlation in the systems and that in the environments, and the quantum correlation in the systems will be transferred into the environments completely and asymptotically.

Key words: quantum correlation, geometric measure

中图分类号: (Decoherence; open systems; quantum statistical methods)

03.65.Yz

03.65.Ta (Foundations of quantum mechanics; measurement theory) 03.67.-a (Quantum information)

蒋峰建, 吕海江, 闫新虎, 石名俊. Symmetric geometric measure and dynamics of quantum discord[J]. 中国物理B, 2013, 22(4): 40303-040303.

Jiang Feng-Jian (蒋峰建), Lü Hai-Jiang (吕海江), Yan Xin-Hu (闫新虎), Shi Ming-Jun (石名俊). Symmetric geometric measure and dynamics of quantum discord[J]. Chin. Phys. B, 2013, 22(4): 40303-040303.

参考文献 53

[1]	Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[2]	Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[3]	Bennett C H, DiVincenzo D, Fuchs C, Mor T, Rains E, Shor P, Smolin J and Wootters W 1999 Phys. Rev. A 59 1070
[4]	Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A and Wootters W 1993 Phys. Rev. Lett. 70 1895
[5]	Bennett C H and Wiesner S 1992 Phys. Rev. Lett. 69 2881
[6]	Braunstein S, Caves C, Jozsa R, Linden N, Popescu S and Schack R 1999 Phys. Rev. Lett. 83 1054
[7]	Meyer D 2000 Phys. Rev. Lett. 85 2014
[8]	Vidal G 2003 Phys. Rev. Lett. 91 147902
[9]	Biham E, Brassard G, Kenigsberg D and Mor T 2004 Theor. Comput. Sci. 320 15
[10]	Knill E and Laflamme R 1998 Phys. Rev. Lett. 81 5672
[11]	Laflamme R, Cory D, Negrevergne C and Viola L 2002 Quantum Inf. Comput. 2 166
[12]	Datta A, Flammia S and Caves C 2005 Phys. Rev. A 72 042316
[13]	Datta A and Vidal G 2007 Phys. Rev. A 75 042310
[14]	Henderson L and Vedral V 2001 J. Phys. A: Math. Gen. 34 6899
[15]	Ollivier H and Zurek W 2001 Phys. Rev. Lett. 88 017901
[16]	Oppenheim J, Horodecki M, Horodecki P and Horodecki R 2002 Phys. Rev. Lett. 89 180402
[17]	Koashi M and Winter A 2004 Phys. Rev. A 69 022309
[18]	Wang L C, Shen J and Yi X X 2011 Chin. Phys. B 20 050306
[19]	Groisman B, Popescu S and Winter A 2005 Phys. Rev. A 72 032317
[20]	Horodecki M, Horodecki P, Horodecki R, Oppenheim J, SenDe A, Sen U and Synak-Radtke B 2005 Phys. Rev. A 71 062307
[21]	Luo S 2008 Phys. Rev. A 77 022301
[22]	Rodríguez-Rosario C, Modi K, Kuah A, Shaji A and Sudarshan E C G 2008 J. Phys. A: Math. Theor. 41 205301
[23]	Shabani A and Lidar D 2009 Phys. Rev. Lett. 102 100402
[24]	Piani M, Horodecki P and Horodecki R 2008 Phys. Rev. Lett. 100 090502
[25]	Piani M, Christandl M, Mora C E and Horodecki P 2009 Phys. Rev. Lett. 102 250503
[26]	Modi K, Paterek T, Son W, Vedral V and Williamson M 2010 Phys. Rev. Lett. 104 080501
[27]	Dakić B, Vedral V and Brukner \vC 2010 Phys. Rev. Lett. 105 190502
[28]	Adesso G and Datta A 2010 Phys. Rev. Lett. 105 030501
[29]	Luo S and Fu S 2011 Phys. Rev. Lett. 106 120401
[30]	Cavalcanti D, Aolita L, Boixo S, Modi K, Piani M and Winter A 2011 Phys. Rev. A 83 032324
[31]	Madhok V and Datta A 2011 Phys. Rev. A 83 032323
[32]	Streltsov A, Kampermann H and Bruβ D 2011 Phys. Rev. Lett. 106 160401
[33]	Piani M, Gharibian S, Adesso G, Calsamiglia J, Horodecki P and Winter A 2011 Phys. Rev. Lett. 106 220403
[34]	Datta A, Shaji A and Caves C 2008 Phys. Rev. Lett. 100 050502
[35]	Merali Z 2011 Nature 474 24
[36]	Miranowicz Adam, Horodecki Pawel, Chhajlany Ravindra W, Tuziemski Jan and Sperling Jan 2012 Phys. Rev. A 86 042123
[37]	Terhal B, Horodecki M, Leung D and DiVincenzo D 2002 J. Math. Phys. 43 4286
[38]	Yu T and Eberly J 2004 Phys. Rev. Lett. 93 140404
[39]	Eberly J and Yu T 2007 Science 316 555
[40]	Yu T and Eberly J 2009 Science 323 598
[41]	Mazzola L, Piilo J and Maniscalco S 2010 Phys. Rev. Lett. 104 200401
[42]	Maziero J, Céleri L, Serra R and Vedral V 2009 Phys. Rev. A 80 044102
[43]	Maziero J, Werlang T, Fanchini F, Céleri L and Serra R 2010 Phys. Rev. A 81 022116
[44]	Werlang T, Souza S, Fanchini F and Boas C 2009 Phys. Rev. A 80 024103
[45]	Wang B, Xu Z, Chen Z and Feng M 2010 Phys. Rev. A 81 014101
[46]	Fanchini F, Werlang T, Brasil C, Arruda L and Caldeira A 2010 Phys. Rev. A 81 052107
[47]	Bengtsson I and Życzkowski K 2006 Geometry of Quantum State: An Introduction to Quantum Entanglement (Cambridge: Cambridge University Press)
[48]	Breuer H P and Petruccione F 2002 The Theory of Open Quantum System (Oxford: Oxford University Press)
[49]	Luo S and Fu S 2010 Phys. Rev. A 82 034302
[50]	Lu X M, Xi Z, Sun Z and Wang X 2010 Quantum Inf. Comput. 10 994
[51]	Ciccarello F and Giovannetti V 2011 arXiv: quant-ph/1105.5551
[52]	Streltsov A, Kampermann H and Bru? D 2011 Phys. Rev. Lett. 107 170502
[53]	Ferraro A, Aolita L, Cavalcanti D, Cucchietti F and Acín A 2010 Phys. Rev. A 81 052318

Symmetric geometric measure and dynamics of quantum discord

Symmetric geometric measure and dynamics of quantum discord

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 53

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Ye-Qi Zhang(张业奇), Xiao-Ting Ding(丁潇婷), Jiao Sun(孙娇), and Tian-Hu Wang(王天虎). Quantum steerability of two qubits mediated by one-dimensional plasmonic waveguides[J]. 中国物理B, 2022, 31(12): 120305-120305.
[2]	Ying-Yue Yang(杨颖玥), Li-Juan Li(李丽娟), Liu Ye(叶柳), and Dong Wang(王栋). Quantum correlation and entropic uncertainty in a quantum-dot system[J]. 中国物理B, 2022, 31(10): 100303-100303.
[3]	Zhen-Yu Chen(陈祯羽), Tian-Hui Qiu(邱田会), Wen-Bin Zhang(张文彬), and Hong-Yang Ma(马鸿洋). Effects of initial states on the quantum correlations in the generalized Grover search algorithm[J]. 中国物理B, 2021, 30(8): 80303-080303.
[4]	杨豪, 秦立国, 田立君, 马鸿洋. Quantum coherence and correlation dynamics of two-qubit system in spin bath environment[J]. 中国物理B, 2020, 29(4): 40303-040303.
[5]	Mohamed Amazioug, Larbi Jebli, Mostafa Nassik, Nabil Habiballah. Quantifying non-classical correlations under thermal effects in a double cavity optomechanical system[J]. 中国物理B, 2020, 29(2): 20304-020304.
[6]	刘堂昆, 刘飞, 单传家, 刘继兵. Geometrical quantum discord and negativity of two separable and mixed qubits[J]. 中国物理B, 2019, 28(9): 90304-090304.
[7]	查新未, 苗宁, 李轲. Relations between tangle and I concurrence for even n-qubit states[J]. 中国物理B, 2019, 28(12): 120304-120304.
[8]	秦猛, 任中洲, 张欣. Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems[J]. 中国物理B, 2018, 27(6): 60301-060301.
[9]	尹少英, 刘庆欣, 宋杰, 许学新, 周可雅, 刘树田. Quantum correlations dynamics of three-qubit states coupled to an XY spin chain:Role of coupling strengths[J]. 中国物理B, 2017, 26(10): 100501-100501.
[10]	杜少将, 夏云杰, 段德洋, 张路, 高强. Optimizing quantum correlation dynamics by weak measurement in dissipative environment[J]. , 2015, 24(4): 44205-044205.
[11]	王冬梅, 钱懿, 许晶波, 俞攸红. Dynamical decoupling pulses on the quantum correlations for the system of superconducting quantum circuit[J]. 中国物理B, 2015, 24(11): 110304-110304.
[12]	刘辛, 吴薇. Rise of quantum correlations in non-Markovian environments in continuous-variable systems[J]. , 2014, 23(7): 70303-070303.
[13]	沈诚诰, 张国锋, 樊开明, 朱汉杰. Measurement-induced disturbance in Heisenberg XY spin model with Dzialoshinskii-Moriya interaction under intrinsic decoherence[J]. 中国物理B, 2014, 23(5): 50310-050310.
[14]	杨阳, 王安民. Correlation dynamics of a qubit–qutrit system in a spin-chain environment with Dzyaloshinsky–Moriya interaction[J]. 中国物理B, 2014, 23(2): 20307-020307.
[15]	李艳杰, 刘金明, 张燕. Quantum correlation switches for dipole arrays[J]. , 2014, 23(11): 110306-110306.