Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice
Abstract
A two-dimensional discrete-time quantum walk (DTQW) can be realized by alternating a two-state DTQW in one spatial dimension followed by an evolution in the other dimension. This was shown to reproduce a probability distribution for a certain configuration of a four-state DTQW on a two-dimensional lattice. In this work we present a three-state alternate DTQW with a parameterized coin-flip operator and show that it can produce localization that is also observed for a certain other configuration of the four-state DTQW and non-reproducible using the two-state alternate DTQW. We will present two limit theorems for the three-state alternate DTQW. One of the limit theorems describes a long-time limit of a return probability, and the other presents a convergence in distribution for the position of the walker on a rescaled space by time. We will also outline the relevance of these walks in physical systems.
Keywords
Cite
@article{arxiv.1510.02885,
title = {Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice},
author = {Takuya Machida and C. M. Chandrashekar},
journal= {arXiv preprint arXiv:1510.02885},
year = {2015}
}
Comments
11 pages, 7 figures