dorsal/arxiv
View SchemaPseudo Memory Effects, Majorization and Entropy in Quantum Random Walks
| Authors | Anthony J. Bracken, Demosthenes Ellinas, Ioannis Tsohantjis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402187 |
| URL | https://arxiv.org/abs/quant-ph/0402187 |
| DOI | 10.1088/0305-4470/37/8/L02 |
| Journal | J. Phys. A : Math. Gen. 37 (2004) L91-L97 |
Abstract
A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.
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"abstract": "A quantum random walk on the integers exhibits pseudo memory effects, in that\nits probability distribution after N steps is determined by reshuffling the\nfirst N distributions that arise in a classical random walk with the same\ninitial distribution. In a classical walk, entropy increase can be regarded as\na consequence of the majorization ordering of successive distributions. The\nLorenz curves of successive distributions for a symmetric quantum walk reveal\nno majorization ordering in general. Nevertheless, entropy can increase, and\ncomputer experiments show that it does so on average. Varying the stages at\nwhich the quantum coin system is traced out leads to new quantum walks,\nincluding a symmetric walk for which majorization ordering is valid but the\nspreading rate exceeds that of the usual symmetric quantum walk.",
"arxiv_id": "quant-ph/0402187",
"authors": [
"Anthony J. Bracken",
"Demosthenes Ellinas",
"Ioannis Tsohantjis"
],
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"quant-ph"
],
"doi": "10.1088/0305-4470/37/8/L02",
"journal_ref": "J. Phys. A : Math. Gen. 37 (2004) L91-L97",
"title": "Pseudo Memory Effects, Majorization and Entropy in Quantum Random Walks",
"url": "https://arxiv.org/abs/quant-ph/0402187"
},
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