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Non-Markovian Decoherent Quantum Walks

Quantum walk acts obviously different from its classical counterpart, but decoherence will lessen and close the gap between them. To understand this process, it is necessary to investigate the evolution of quantum walk under different situation 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 quantum walk starts oscillating from the first several steps and tends to be linear on time and showing a diffusive spread in the long time limit, which is caused by the non-Markovian dephasing affecting on quantum correlations between quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of quantum correlations and observe that both of them oscillate in the short time regime and tend to be zero in the long time limit. Therefore quantum walk with 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.