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arXiv:quant-ph/0309135 · Physical Review E

Weak limits for quantum random walks

Geoffrey Grimmett, Svante Janson, Petra F. Scudo

Published Feb 27, 2004• 223 citations
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Abstract

We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With X(n) denoting position at time n, we show that X(n)/n converges weakly as n--> infinity to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain preceding derivations valid in one dimension that make use of combinatorial and path integral methods.

DOI
10.1103/physreve.69.026119

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We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With X(n) denoting position at time n, we show that X(n)/n converges weakly as n--> infinity to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain preceding derivations valid in one dimension that make use of combinatorial and path integral methods.
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