| Autor: |
Stefanak, M., Kollar, B., Kiss, T., Jex, I. |
| Rok vydání: |
2010 |
| Předmět: |
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| Zdroj: |
Phys. Scr. T140, 014035 (2010) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1088/0031-8949/2010/T140/014035 |
| Popis: |
Recurrence of a random walk is described by the Polya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full-revival of its quantum state. Localization for two dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show on the example of the 2-D Grover walk that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full-revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference which has no counterpart in classical random walks. |
| Databáze: |
arXiv |
| Externí odkaz: |
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