Quantum speed limits for Bell-diagonal states

doi:10.1088/1674-1056/24/12/120304

Abstract The lower bounds of the evolution time between two distinguishable states of a system, defined as quantum speed limit time, can characterize the maximal speed of quantum computers and communication channels. We study the quantum speed limit time between the composite quantum states and their target states in the presence of nondissipative decoherence. For the initial states with maximally mixed marginals, we obtain the exact expressions of the quantum speed limit time which mainly depend on the parameters of the initial states and the decoherence channels. Furthermore, by calculating the quantum speed limit time for the time-dependent states started from a class of initial states, we discover that the quantum speed limit time gradually decreases in time, and the decay rate of the quantum speed limit time would show a sudden change at a certain critical time. Interestingly, at the same critical time, the composite system dynamics would exhibit a sudden transition from classical decoherence to quantum decoherence.

Keywords: quantum information quantum decoherence quantum speed limit time

Received: 09 July 2015
Revised: 25 August 2015
Accepted manuscript online:

PACS:	03.65.Yz	(Decoherence; open systems; quantum statistical methods)
	03.67.Lx	(Quantum computation architectures and implementations)
	42.50.-p	(Quantum optics)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61178012 and 11304179), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant Nos. 20123705120002 and 20133705110001), the Natural Science Foundation of Shandong Province of China (Grant No. ZR2014AP009), and the Scientific Research Foundation of Qufu Normal University.

Corresponding Authors: Zhang Ying-Jie
E-mail: yingjiezhang@mail.qfnu.edu.cn

Cite this article:

Han Wei (韩伟), Jiang Ke-Xia (江克侠), Zhang Ying-Jie (张英杰), Xia Yun-Jie (夏云杰) Quantum speed limits for Bell-diagonal states 2015 Chin. Phys. B 24 120304

[1]	Bekenstein J D 1981 Phys. Rev. Lett. 46 623
[2]	Zheng S B 2010 Chin. Phys. B 19 064204
[3]	Giovanetti V, Lloyd S and Maccone L 2011 Nat. Photon. 5 222
[4]	Xiang G Y and Guo G C 2013 Chin. Phys. B 22 110601
[5]	Lloyd S 2002 Phys. Rev. Lett. 88 237901
[6]	Caneva T, Murphy M, Calarco T, Fazio R, Montangero S, Giovannetti V and Santoro G E 2009 Phys. Rev. Lett. 103 240501
[7]	Barnes E 2013 Phys. Rev. A 88 013808
[8]	Hegerfeldt G C 2013 Phys. Rev. Lett. 111 260501
[9]	Poggi P M, Lombardo F C and Wisniacki D A 2013 Europhys. Lett. 104 4005
[10]	Mandelstam L and Tamm I 1945 J. Phys. (USSR) 9 249
[11]	Fleming G N 1973 Nuovo Cimento A 16 232
[12]	Anandan J and Aharonov Y 1990 Phys. Rev. Lett. 65 1697
[13]	Vaidman L 1992 Am. J. Phys. 60 182
[14]	Margolus N and Levitin L B 1998 Physica D 120 188
[15]	Levitin L B and Toffoli T 2009 Phys. Rev. Lett. 103 160502
[16]	Giovannetti V, Lloyd S and Maccone L 2003 Phys. Rev. A 67 052109
[17]	Jones P and Kok P 2010 Phys. Rev. A 82 022107
[18]	Zwierz M 2012 Phys. Rev. A 86 016101
[19]	Deffner S and Lutz E 2013 J. Phys. A: Math. Theor. 46 335302
[20]	Pfeifer P 1993 Phys. Rev. Lett. 70 3365
[21]	Pfeifer P and Fröhlich J 1995 Rev. Mod. Phys. 67 759
[22]	Taddei M M, Escher B M, Davidovich L and de Matos Filho R L 2013 Phys. Rev. Lett. 110 050402
[23]	del Campo A, Egusquiza I L, Plenio M B and Huelga S F 2013 Phys. Rev. Lett. 110 050403
[24]	Deffner S and Lutz E 2013 Phys. Rev. Lett. 111 010402
[25]	Zhang Y J, Han W, Xia Y J, Cao J P and Fan H 2014 Sci. Rep. 4 4890
[26]	Xu Z Y, Luo S, Yang W L, Liu C and Zhu S Q 2014 Phys. Rev. A 89 012307
[27]	Zhang Y J, Han W, Xia Y J, Cao J P and Fan H 2015 Phys. Rev. A 91 032112
[28]	Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[29]	Bennett C H and Divincenzo D P 2000 Nature 404 247
[30]	Xu J S, Sun K, Li C F, Xu X Y, Guo G C, Andersson E, Lo Franco R and Compagno G 2013 Nat. Commun. 4 2851
[31]	Aaronson B, Lo Franco R and Adesso G 2013 Phys. Rev. A 88 012120
[32]	Zhang Y J, Zou X B, Xia Y J and Guo G C 2010 Phys. Rev. A 82 022108
[33]	Duan L M, Lukin M D, Cirac J I and Zoller P 2001 Nature 414 413
[34]	Sheng Y B, Zhou L, Cheng W W, Gong L X, Zhao S M and Zheng B Y 2012 Chin. Phys. B 21 030307
[35]	Cirac J I and Zoller P 2012 Nat. Phys. 8 264
[36]	Georgescu I M, Ashhab S and Nori F 2014 Rev. Mod. Phys. 86 153
[37]	Mazzola L, Piilo J and Maniscalco S 2010 Phys. Rev. Lett. 104 200401
[38]	Salles A, de Melo F, Almeida M P, Hor-Meyll M, Walborn S P, Souto Ribeiro P H and Davidovich L 2008 Phys. Rev. A 78 022322
[39]	Luo S 2008 Phys. Rev. A 77 042303

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