Quantum and random walks as universal generators of probability distributions
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a bell-shaped one in the second case. Here I show how one can impose a...
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2017 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/112789 |
| Acesso em linha: | https://hdl.handle.net/2445/112789 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Rutes aleatòries (Matemàtica) Distribució (Teoria de la probabilitat) Processos estocàstics Random walks (Mathematics) Distribution (Probability theory) Stochastic processes |
| Resumo: | Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a bell-shaped one in the second case. Here I show how one can impose any desired stochastic behavior (compatible with the continuity equation for the probability function) on both systems by the appropriate choice of time- and site-dependent coins. This implies, in particular, that one can devise quantum walks that show diffusive spreading without losing coherence as well as random walks that exhibit the characteristic fast propagation of a quantum particle driven by a Hadamard coin. |
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