paper

The quantum to classical transition for random walks

arXiv:quant-ph/0208195 · doi:10.1103/PhysRevLett.91.130602

Abstract

We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference. We use the position variance as an indicator of classical behavior, and find analytical expressions for this in the long-time limit; we see that the multicoin walk retains the ``quantum'' quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits ``classical'' linear growth of the variance even for weak decoherence.

4 pages RevTeX 4.0 + 2 figures (encapsulated Postscript). Trimmed for length. Minor corrections + one new reference

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