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<p>In this work, we study the problem of obtaining invariant distributions of quantum Markov chains (QMCs), which are given by positive maps acting on appropriate trace-class spaces. We focus on discrete time statistics for the integer half-line and discuss the notions of fair coin and positive recurrence in such context. Inspired by the theory of quasi-birth-and-death processes as described by G. Latouche and V. Ramaswami, we study a basic algorithm for obtaining the individual entries of distributions of QMCs, describe concrete examples and make comparisons with the classical setting.</p>

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Invariant distributions of 1-dimensional homogeneous quantum Markov chains: procedure and examples

  • 期刊论文

  • 发表日期：

    2025年9月23日

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  • C. F. Lardizabal

摘要

In this work, we study the problem of obtaining invariant distributions of quantum Markov chains (QMCs), which are given by positive maps acting on appropriate trace-class spaces. We focus on discrete time statistics for the integer half-line and discuss the notions of fair coin and positive recurrence in such context. Inspired by the theory of quasi-birth-and-death processes as described by G. Latouche and V. Ramaswami, we study a basic algorithm for obtaining the individual entries of distributions of QMCs, describe concrete examples and make comparisons with the classical setting.