Weak limits for quantum random walks
- 27 February 2004
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 69 (2), 026119
- https://doi.org/10.1103/physreve.69.026119
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 $n \to \infty$ 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
Keywords
This publication has 2 references indexed in Scilit:
- Quantum random walks: An introductory overviewContemporary Physics, 2003
- Quantum Random Walks in One DimensionQuantum Information Processing, 2002