Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(7): 070302    DOI: 10.1088/1674-1056/22/7/070302
GENERAL Prev   Next  

Non-Markovian decoherent quantum walks

Xue Peng (薛鹏)a, Zhang Yong-Sheng (张永生)b
a Department of Physics, Southeast University, Nanjing 211189, China;
b Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
Abstract  Quantum walk acts obviously different from its classical counterpart, but the decoherence will lessen and close the gap between them. To understand this process, it is necessary to investigate the evolution of the quantum walk under different situations of decoherence. In this article, we study a non-Markovian decoherent quantum walk on a line. In the short time regime, the behavior of the walk deviates from both idea quantum walks and classical random walks. The position variance as a measure of the quantum-walk collapses and revivals for a short time and tends to have a linear relation with time, that is the walker's behavior shows a diffusive spread in the long time limit, which is caused by the non-Markovian dephasing affecting on quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of quantum correlations and observe that both collapse and revival in the short time regime and tend to be zero in the long time limit. Therefore, the quantum walk with a non-Markovian decoherence tends to diffusive spreading behavior in the long time limit, while in the short time regime, it oscillates between a ballistic and diffusive spreading behavior, and the quantum correlation collapses and revivals due to the memory effect.
Keywords:  non-Markovian decohernece      quantum walks      quantum correlations  
Received:  11 December 2012      Revised:  28 February 2013      Accepted manuscript online: 
PACS:  03.67.Mn (Entanglement measures, witnesses, and other characterizations)  
  03.65.Ta (Foundations of quantum mechanics; measurement theory)  
  05.40.Fb (Random walks and Levy flights)  
  03.67.Ac (Quantum algorithms, protocols, and simulations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10974192, 11004029, and 11174052), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010422), the Ph.D. Program of the Ministry of Education of China, the Excellent Young Teachers Program of Southeast University, China, and the National Basic Research Development Program of China (Grant No. 2011CB921203).
Corresponding Authors:  Xue Peng     E-mail:  gnep.eux@gmail.com

Cite this article: 

Xue Peng (薛鹏), Zhang Yong-Sheng (张永生) Non-Markovian decoherent quantum walks 2013 Chin. Phys. B 22 070302

[1] Xue P 2011 Chin. Phys. B 20 100310
[2] Xue P 2012 Chin. Phys. B 21 010308
[3] Xue P 2012 Chin. Phys. B 21 100306
[4] Aharonov D, Ambainis A, Kempe J and Vazirani U 2001 Proceedings of the 33rd ACM Symposium on the Theory of Computing, 2001, ACM, Washington, DC, p. 50
[5] Kendon V 2006 Math. Struct. Comput. Sci. 17 1
[6] Childs A M, Cleve R, Deotto E, Farhi E, Gutmann S and Spielman D A 2003 Proceedings of the 35th ACM Symposium on the Theory of Computing, 2003, ACM, Washington, DC, p. 59
[7] Ryan C A, Laforest M, Boilequ J C and Laflamme R 2005 Phys. Rev. A 72 062317
[8] Du J, Li H, Xu X, Shi M, Wu J, Zhou X and Han R 2003 Phys. Rev. A 67 042316
[9] Zähringer F, Kirchmair G, Gerritsma R, Solano E, Blatt R and Roos C F 2010 Phys. Rev. Lett. 104 100503
[10] Do B, Stohler M, Balasubramanian S and Elliott D 2005 J. Opt. Soc. Am. B 22 499
[11] Schreiber A, Cassemiro K N, Potoček V, Gábris A, Mosley P J, Andersson E, Jex I and Silberhorn C 2010 Phys. Rev. Lett. 104 050502
[12] Broome M A, Fedrizzi A, Lanyon B P, Kassal I, Aspuru-Guzik A and White A G 2010 Phys. Rev. Lett. 104 153602
[13] Schreiber A, Cassemiro K N, Potoček V, Gábris A, Jex I and Silberhorn C 2011 Phys. Rev. Lett. 106 180403
[14] Perets H B, Lahini Y, Pozzi F, Sorel M, Morandotti R and Silberberg Y 2008 Phys. Rev. Lett. 100 170506
[15] Brun T, Carteret H A and Ambainis A 2003 Phys. Rev. Lett. 91 130602
[16] Brun T, Carteret H A and Ambainis A 2003 Phys. Rev. A 67 052317
[17] Xue P and Sanders B C 2008 New J. Phys. 8 053025
[18] Xue P, Sanders B C, Blais A and Lalumiére K 2008 Phys. Rev. A 78 042334
[19] Xue P, Sanders B C and Leibfried D 2009 Phys. Rev. Lett. 103 183602
[20] Xue P and Sanders B C 2012 Phys. Rev. A 85 022307
[21] Xu Y Y, Zhou F, Chen L, Xie Y, Xue P and Feng M 2012 Chin. Phys. B 21 040304
[22] Li M, Zhang Y S and Guo C G 2013 Chin. Phys. B 22 030310
[23] Carmichael H J 1993 An Open Systems Approach to Quantum Optics (Berlin: Springer-Verlag)
[24] Weiss U 2001 Quantum Dissipative Systems (Singapore: World Scientific)
[25] Kempe J 2003 Contemp. Phys. 44 307
[26] Shenvi N, Kempe J and Whaley K B 2003 Phys. Rev. A 67 052307
[27] Wolf M M, Eisert J, Cubitt T S and Cirac J I 2008 Phys. Rev. Lett. 101 150402
[28] Bellomo B, Franco R and Compagno G 2007 Phys. Rev. Lett. 99 160502
[29] Rivas A, Huelga S F and Plenio M B 2010 Phys. Rev. Lett. 105 050403
[30] Laine E, Piilo J and Breuer H 2010 Phys. Rev. A 81 062115
[31] Breuer H, Laine E and Piilo J 2009 Phys. Rev. Lett. 103 210401
[32] Raimond J M, Brune M and Haroche S 1997 Phys. Rev. Lett. 79 1964
[33] Meunier T, Gleyzes S, P. Maioli P, Auffeves A, Nogues G, Brune M, Raimond J M and Haroche S 2005 Phys. Rev. Lett. 94 010401
[34] Xu J S, Li C F, Gong M, Zou X B, Shi C H, Chen G and Guo G C 2010 Phys. Rev. Lett. 104 100502
[35] Xu J S, Li C F, Zhang C J, Xu X Y, Zhang Y S and Guo G C 2010 Phys. Rev. A 82 042328
[36] Tang J S, Li C F, Li Y L, Zou X B, Guo G C, Breuer H, Laine E and Piilo J 2012 Europhys. Lett. 97 10002
[37] Liu B H, Li L, Huang Y F, Li C F, Guo G C, Laine E, Breuer H and Piilo J 2011 Nat. Phys. 7 931
[38] Luo S 2008 Phys. Rev. A 77 022301
[39] Li N and Luo S 2007 Phys. Rev. A 76 032327
[40] Luo S 2008 Phys. Rev. A 77 042303
[41] Ollivier H and Zurek W H 2001 Phys. Rev. Lett. 88 017901
[42] Henderson L and Vedral V 2001 J. Phys. A 34 6899
[43] Srikanth R, Banerjee S and Chandrashekar C M 2010 Phys. Rev. A 81 062123
[44] Rao B R, Srikanth R, Chandrashekar C M and Banerjee S 2011 Phys. Rev. A 83 064302
[1] Efficient quantum private comparison protocol based on one direction discrete quantum walks on the circle
Jv-Jie Wang(王莒杰), Zhao Dou(窦钊), Xiu-Bo Chen(陈秀波), Yu-Ping Lai(赖裕平), and Jian Li(李剑). Chin. Phys. B, 2022, 31(5): 050308.
[2] Quantum steerability of two qubits mediated by one-dimensional plasmonic waveguides
Ye-Qi Zhang(张业奇), Xiao-Ting Ding(丁潇婷), Jiao Sun(孙娇), and Tian-Hu Wang(王天虎). Chin. Phys. B, 2022, 31(12): 120305.
[3] Disorder in parity-time symmetric quantum walks
Peng Xue(薛鹏). Chin. Phys. B, 2022, 31(1): 010311.
[4] Effects of initial states on the quantum correlations in the generalized Grover search algorithm
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). Chin. Phys. B, 2021, 30(8): 080303.
[5] Quantifying non-classical correlations under thermal effects in a double cavity optomechanical system
Mohamed Amazioug, Larbi Jebli, Mostafa Nassik, Nabil Habiballah. Chin. Phys. B, 2020, 29(2): 020304.
[6] A two-dimensional quantum walk driven by a single two-side coin
Quan Lin(林泉), Hao Qin(秦豪) Kun-Kun Wang(王坤坤), Lei Xiao(肖磊), and Peng Xue(薛鹏). Chin. Phys. B, 2020, 29(11): 110303.
[7] Relations between tangle and I concurrence for even n-qubit states
Xin-Wei Zha(查新未), Ning Miao(苗宁), Ke Li(李轲). Chin. Phys. B, 2019, 28(12): 120304.
[8] The entanglement of deterministic aperiodic quantum walks
Ting-Ting Liu(刘婷婷), Ya-Yun Hu(胡亚运), Jing Zhao(赵静), Ming Zhong(钟鸣), Pei-Qing Tong(童培庆). Chin. Phys. B, 2018, 27(12): 120305.
[9] A quantum walk in phase space with resonator-assisted double quantum dots
Zhi-Hao Bian(边志浩), Hao Qin(秦豪), Xiang Zhan(詹翔), Jian Li(李剑), Peng Xue(薛鹏). Chin. Phys. B, 2016, 25(2): 020307.
[10] Localization of quantum walks on finite graphs
Yang-Yi Hu(胡杨熠), Ping-Xing Chen(陈平形). Chin. Phys. B, 2016, 25(12): 120303.
[11] Quantum walks with coins undergoing different quantum noisy channels
Hao Qin(秦豪) and Peng Xue(薛鹏). Chin. Phys. B, 2016, 25(1): 010501.
[12] Dynamical decoupling pulses on the quantum correlations for the system of superconducting quantum circuit
Wang Dong-Mei (王冬梅), Qian Yi (钱懿), Xu Jing-Bo (许晶波), Yu You-Hong (俞攸红). Chin. Phys. B, 2015, 24(11): 110304.
[13] Measurement-induced disturbance in Heisenberg XY spin model with Dzialoshinskii-Moriya interaction under intrinsic decoherence
Shen Cheng-Gao (沈诚诰), Zhang Guo-Feng (张国锋), Fan Kai-Ming (樊开明), Zhu Han-Jie (朱汉杰). Chin. Phys. B, 2014, 23(5): 050310.
[14] Implementation of a one-dimensional quantum walk in both position and phase spaces
Qin Hao (秦豪), Xue Peng (薛鹏). Chin. Phys. B, 2014, 23(1): 010301.
[15] Quantum correlation of a three-particle W-class state under quantum decoherence
Xu Peng (许鹏), Wang Dong (王栋), Ye Liu (叶柳). Chin. Phys. B, 2013, 22(10): 100306.
No Suggested Reading articles found!