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arXiv · 2402.15878

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

Manuel D. De la Iglesia·Carlos F. Lardizabal
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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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Manuel D. De la Iglesia, Carlos F. Lardizabal. 2024-02-24. One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures. https://doi.org/10.1088/1751-8121%2Fad5bcb

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