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.

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).

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