Weak limits for quantum random walks

Details Weak limits for quantum random walks Weak limits for quantum random walks

2003-09-18

arxiv.org/abs/quant-ph/0309135v1

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevE.69.026119

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 $n \to \infty$ 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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