Discrete-time quantum walk with time-correlated noise

We investigate the dynamics of discrete-time quantum walk subject to time correlated noise. Noise is described as an unitary coin-type operator before each step, and attention focused on noise generated by a Gaussian Ornstein Uhlenbeck process, going beyond usual telegraph noise, where random variables are consist only -1 1. Under first-order approximation BCH formula, master equation noisy derived. The given in good agreement with those numerical simulations within certain period steps, which controlled parameters. Two remarker behaviors long observed simulations, corresponding two opposite regimes: slow regime, increase amplitude, coherence suppressed, gradually transits that classical walk. In fast walker confined into few lattice sites, width wave packet much narrower compared regime.