An algebraic structure for one-dimensional quantum walks and a new proof of the weak limit theorem
Functional Analysis
2017-11-15 v2 Classical Analysis and ODEs
Abstract
An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula for the characteristic function of the transition probability. Then, the weak limit theorem for the transition probability of quantum walks is deduced by using simple properties of the Chebyshev polynomials.
Keywords
Cite
@article{arxiv.1210.0631,
title = {An algebraic structure for one-dimensional quantum walks and a new proof of the weak limit theorem},
author = {Tatsuya Tate},
journal= {arXiv preprint arXiv:1210.0631},
year = {2017}
}
Comments
10 pages. The title has been changed. The abstract has been rewritten