The effect of unitary noise on the discrete one-dimensional quantum walk was studied. It was shown that when the quantum walk is exposed to unitary noise it exhibits a crossover from the quantum behavior for short times to classical-like behavior for long times. For times shorter than the crossover time, the standard deviation σα(t) of the spatial distribution of the noisy Hadamard walk, scaled linearly with t, like the noiseless Hadamard walk.
|Physical Review A - Atomic, Molecular, and Optical Physics
|Published - Dec 2003