Probability distributions and weak limit theorems of quaternionic quantum walks in one dimension
Quantum Physics
2019-01-30 v3 Probability
Abstract
The discrete-time quantum walk (QW) is determined by a unitary matrix whose component is complex number. Konno (2015) extended the QW to a walk whose component is quaternion.We call this model quaternionic quantum walk (QQW). The probability distribution of a class of QQWs is the same as that of the QW. On the other hand, a numerical simulation suggests that the probability distribution of a QQW is different from the QW. In this paper, we clarify the difference between the QQW and the QW by weak limit theorems for a class of QQWs.
Keywords
Cite
@article{arxiv.1710.01482,
title = {Probability distributions and weak limit theorems of quaternionic quantum walks in one dimension},
author = {Kei Saito},
journal= {arXiv preprint arXiv:1710.01482},
year = {2019}
}
Comments
11 pages, 2 figures, Interdisciplinary Information Sciences (in press)