Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators
Quantum Physics
2024-03-07 v1
Abstract
We study continuous-time open quantum walks in one dimension through a matrix representation, focusing on nearest-neighbor transitions for which an associated weight matrix exists. Statistics such as site recurrence are studied in terms of matrix-valued orthogonal polynomials and explicit calculations are obtained for classes of Lindblad generators that model quantum versions of birth-death processes. Emphasis is given to the technical distinction between the cases of a finite or infinite number of vertices. Recent results for open quantum walks are adapted in order to apply the folding trick to continuous-time birth-death chains on the integers. Finally, we investigate the matrix-valued Stieltjes transform associated to the weights.
Cite
@article{arxiv.2311.16366,
title = {Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators},
author = {Newton Loebens},
journal= {arXiv preprint arXiv:2311.16366},
year = {2024}
}