Stationary measure for three-state quantum walk
Mathematical Physics
2019-09-04 v2 math.MP
Probability
Abstract
We focus on the three-state quantum walk(QW) in one dimension. In this paper, we give the stationary measure in general condition, originated from the eigenvalue problem. Firstly, we get the transfer matrices by our new recipe, and solve the eigenvalue problem. Then we obtain the general form of the stationary measure for concrete initial state and eigenvalue. We also show some specific examples of the stationary measure for the three-state QW. One of the interesting and crucial future problems is to make clear the whole picture of the set of stationary measures.
Keywords
Cite
@article{arxiv.1903.01615,
title = {Stationary measure for three-state quantum walk},
author = {Takako Endo and Takashi Komatsu and Norio Konno and Tomoyuki Terada},
journal= {arXiv preprint arXiv:1903.01615},
year = {2019}
}
Comments
12 pages