One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures

• URL: http://arxiv.org/abs/2402.15878v2
• Date: Wed, 20 Nov 2024 11:25:14 GMT
• Title: One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
• Authors: Manuel D. De la Iglesia, Carlos F. Lardizabal,
• Abstract summary: We study continuous-time QMCs on the integer line, half-line and finite segments. We are able to obtain exact probability calculations in terms of the associated matrix-valueds and measures.
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• Abstract: Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal (quantum) degrees of freedom. In this work we study continuous-time QMCs on the integer line, half-line and finite segments, so that we are able to obtain exact probability calculations in terms of the associated matrix-valued orthogonal polynomials and measures. The methods employed here are applicable to a wide range of settings, but we will restrict to classes of examples for which the Lindblad generators are induced by a single positive map, and such that the Stieltjes transforms of the measures and their inverses can be calculated explicitly.

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