| GENERAL |
|
|
|
|
Dynamics of Open Systems with Affine Maps |
| ZHANG Da-Jian, LIU Chong-Long, TONG Dian-Min** |
| Department of Physics, Shandong University, Jinan 250100 |
|
| Cite this article: |
|
ZHANG Da-Jian, LIU Chong-Long, TONG Dian-Min 2015 Chin. Phys. Lett. 32 040302 |
|
|
|
|
Abstract Many quantum systems of interest are initially correlated with their environments and the reduced dynamics of open systems are an interesting while challenging topic. Affine maps, as an extension of completely positive maps, are a useful tool to describe the reduced dynamics of open systems with initial correlations. However, it is unclear what kind of initial state shares an affine map. In this study, we give a sufficient condition of initial states, in which the reduced dynamics can always be described by an affine map. Our result shows that if the initial states of the combined system constitute a convex set, and if the correspondence between the initial states of the open system and those of the combined system, defined by taking the partial trace, is a bijection, then the reduced dynamics of the open system can be described by an affine map.
|
|
|
Received: 27 January 2015
Published: 30 April 2015
|
|
| PACS: |
03.65.Yz
|
(Decoherence; open systems; quantum statistical methods)
|
| |
03.65.Vf
|
(Phases: geometric; dynamic or topological)
|
| |
03.65.Ca
|
(Formalism)
|
|
|
|
|
|
[1] Lindblad G 1976 Commun. Math. Phys. 48 119
[2] Kraus K 1983 States, Effects and Operations: Fundamental Physics (New York: Spring-Verlag)
[3] Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University)
[4] Pechukas P 1994 Phys. Rev. Lett. 73 1060
[5] Štelmachovi? P and Bu?ek V 2001 Phys. Rev. A 64 062106
Štelmachovi? P and Bu?ek V 2003 Phys. Rev. A 67 029902
[6] Song H S et al 2002 Chin. Phys. Lett. 19 53
[7] Hayashi H, Kimura G and Ota Y 2003 Phys. Rev. A 67 062109
[8] Fonseca Romero K M, Talkner P and Hänggi P 2004 Phys. Rev. A 69 052109
[9] Jordan T F, Shaji A and Sudarshan E C G 2004 Phys. Rev. A 70 052110
[10] Tong D M et al 2004 Phys. Rev. A 69 054102
[11] Jordan T F 2005 Phys. Rev. A 71 034101
[12] Zhang Y, Cao W C and Long G L 2005 Chin. Phys. Lett. 22 2143
[13] Jordan T F, Shaji A and Sudarshan E C G 2006 Phys. Rev. A 73 012106
[14] Carteret H A, Terno D R and ?yczkowski K 2008 Phys. Rev. A 77 042113
[15] Rodriguez-Rosario C A et al 2008 J. Phys. A 41 205301
[16] Sheng Y B, Deng F G and Zhou H Y 2008 Chin. Phys. Lett. 25 3558
[17] Shabani A and Lidar D A 2009 Phys. Rev. Lett. 102 100402
[18] Shabani A and Lidar D A 2009 Phys. Rev. A 80 012309
[19] Rodríguez-Rosario C A, Modi K and Aspuru-Guzik A 2010 Phys. Rev. A 81 012313
[20] Modi K and Sudarshan E C G 2010 Phys. Rev. A 81 052119
[21] Masillo F, Scolarici G and Solombrino L 2011 J. Math. Phys. 52 012101
[22] Xu G F and Tong D M 2011 Chin. Phys. Lett. 28 060305
[23] Modi K, Rodríguez-Rosario C A and Aspuru-Guzik A 2012 Phys. Rev. A 86 064102
[24] Ye B L et al 2013 Chin. Phys. Lett. 30 020302
[25] Brodutch A et al 2013 Phys. Rev. A 87 042301
[26] Dominy J M, Shabani A and Lidar D A arXiv:1312.0908v1
[27] Liu L and Tong D M 2014 Phys. Rev. A 90 012305
[28] Buscemi F 2014 Phys. Rev. Lett. 113 140502
[29] Sudarshan E C G, Mathews P M and Rau J 1961 Phys. Rev. 121 920
[30] Jordan T F and Sudarshan E C G 1961 J. Math. Phys. 2 772
[31] Jordan T F, Pinsky M A and Sudarshan E C G 1962 J. Math. Phys. 3 848
[32] Breuer H P and Petruccione F 2007 The Theory of Open Quantum Systems (Oxford: Oxford University )
[33] Fujiwara A and Algoet P 1999 Phys. Rev. A 59 3290
[34] Ruskai M B, Szarek S and Werner E 2002 Linear Algebra and its Applications 347 159 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
