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, Vol. 91, No. 13 (2003), p. 130602
Main Author: Brun, Todd A (Author)
Other Involved Persons: Carteret, Hilary A ; Ambainis, Andris
Format: Article
Language:English
ISSN:1079-7114
Item Description:Date Completed 25.11.2003
Date Revised 03.10.2003
published: Print-Electronic
Citation Status PubMed-not-MEDLINE
Copyright: From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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520 |a 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 
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