dorsal/arxiv
View SchemaThe quantum to classical transition for random walks
| Authors | Todd A. Brun, Hilary A. Carteret, Andris Ambainis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208195 |
| URL | https://arxiv.org/abs/quant-ph/0208195 |
| DOI | 10.1103/PhysRevLett.91.130602 |
| Journal | Phys. Rev. Lett. 91, 130602 (2003). |
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.
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"abstract": "We look at two possible routes to classical behavior for the discrete quantum\nrandom walk on the line: decoherence in the quantum ``coin\u0027\u0027 which drives the\nwalk, or the use of higher-dimensional coins to dilute the effects of\ninterference. We use the position variance as an indicator of classical\nbehavior, and find analytical expressions for this in the long-time limit; we\nsee that the multicoin walk retains the ``quantum\u0027\u0027 quadratic growth of the\nvariance except in the limit of a new coin for every step, while the walk with\ndecoherence exhibits ``classical\u0027\u0027 linear growth of the variance even for weak\ndecoherence.",
"arxiv_id": "quant-ph/0208195",
"authors": [
"Todd A. Brun",
"Hilary A. Carteret",
"Andris Ambainis"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.91.130602",
"journal_ref": "Phys. Rev. Lett. 91, 130602 (2003).",
"title": "The quantum to classical transition for random walks",
"url": "https://arxiv.org/abs/quant-ph/0208195"
},
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