Quantum to classical transition for random walks

We look at two possible routes to classical behavior for the discrete quantum random walk on the integers: decoherence in the quantum "coin" which drives the walk, or the use of higher-dimensional (or multiple) coins to dilute the effects of interference. We use the position variance as an...

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Bibliographic Details
Published in:Physical review letters 2003-09, Vol.91 (13), p.130602-130602, Article 130602
Main Authors: Brun, Todd A, Carteret, Hilary A, Ambainis, Andris
Format: Article
Language:English
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Summary:We look at two possible routes to classical behavior for the discrete quantum random walk on the integers: decoherence in the quantum "coin" which drives the walk, or the use of higher-dimensional (or multiple) 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.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.91.130602