Lecture notes on classical and quantum non-Markovianity

Abstract:The study of non-Markovian quantum processes has attracted significant interest in recent decades, giving rise to several competing notions of quantum non-Markovianity. These notes serve as an introduction to the topic for graduate students familiar with quantum mechanics and probability theory. Owing to the vastness of the literature, we focus on two prominent characterizations of quantum Markovianity based on the divisibility of quantum channels and monotonically decreasing state distinguishability. The correspondence between classical concepts (stochastic matrices, Chapman-Kolmogorov equation) and their quantum analogs (dynamical maps, CP-divisibility) is emphasized throughout.

40 pages, 3 figures, accepted version. Invited submission to Lectures from the 33rd Chris Engelbrecht Summer School, Stellenbosch 2025

arXiv:2607.07332 [quant-ph]

(or arXiv:2607.07332v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.07332 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1139/cjp-2026-0130 Focus to learn more DOI(s) linking to related resources

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