7 research outputs found
Quantum walks with random phase shifts
We investigate quantum walks in multiple dimensions with different quantum
coins. We augment the model by assuming that at each step the amplitudes of the
coin state are multiplied by random phases. This model enables us to study in
detail the role of decoherence in quantum walks and to investigate the
quantum-to-classical transition. We also provide classical analogues of the
quantum random walks studied. Interestingly enough, it turns out that the
classical counterparts of some quantum random walks are classical random walks
with a memory and biased coin. In addition random phase shifts "simplify" the
dynamics (the cross interference terms of different paths vanish on average)
and enable us to give a compact formula for the dispersion of such walks.Comment: to appear in Phys. Rev. A (10 pages, 5 figures