arXiv:1410.0550 · Physical Review A

Invariance in quantum walks with time-dependent coin operators

Miquel Montero

Published Dec 5, 2014• 11 citations

Abstract

This paper unveils some features of a discrete-time quantum walk on the line whose coin depends on the temporal variable. After considering the most general form of the unitary coin operator, it focuses on the role played by the two phase factors that one can incorporate there, and shows how both terms influence the evolution of the system. A closer analysis reveals that the probabilistic properties of the motion of the walker remain unaltered when the update rule of these phases is chosen adequately. This invariance is based on a symmetry with consequences not yet fully explored.

DOI: 10.1103/physreva.90.062312

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