Non-Markovian decoherent quantum walks

doi:10.1088/1674-1056/22/7/070302

中国物理B ›› 2013, Vol. 22 ›› Issue (7): 70302-070302.doi: 10.1088/1674-1056/22/7/070302

Non-Markovian decoherent quantum walks

薛鹏^a, 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

收稿日期:2012-12-11 修回日期:2013-02-28 出版日期:2013-06-01 发布日期:2013-06-01
基金资助:
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).

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

Received:2012-12-11 Revised:2013-02-28 Online:2013-06-01 Published:2013-06-01
Contact: Xue Peng E-mail:gnep.eux@gmail.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: non-Markovian decohernece, quantum walks, quantum correlations

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.

Key words: non-Markovian decohernece, quantum walks, quantum correlations

中图分类号: (Entanglement measures, witnesses, and other characterizations)

03.67.Mn

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)

薛鹏, 张永生. Non-Markovian decoherent quantum walks[J]. 中国物理B, 2013, 22(7): 70302-070302.

Xue Peng (薛鹏), Zhang Yong-Sheng (张永生). Non-Markovian decoherent quantum walks[J]. Chin. Phys. B, 2013, 22(7): 70302-070302.

参考文献 44

[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

Non-Markovian decoherent quantum walks

Non-Markovian decoherent quantum walks

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