Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators

• URL: http://arxiv.org/abs/2311.16366v1
• Date: Mon, 27 Nov 2023 23:12:51 GMT
• Title: Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators
• Authors: Newton Loebens
• Abstract summary: We study continuous-time open quantum walks in one dimension through a matrix focusing on nearest-neighbor transitions. Recent results for quantum walks are adapted in order to apply the folding trick to continuous-time birth-death chains on the integers.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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