Quantum walks with random phase shifts

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Authors

KOŠÍK Jozef BUŽEK Vladimír HILLERY Mark

Year of publication 2006
Type Article in Periodical
Magazine / Source Physical Review A
MU Faculty or unit

Faculty of Informatics

Citation
Field Theoretical physics
Keywords quantum walk
Description 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 analog 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.
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