2026/01/01 by Graeme Pleasance
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Spectral Theory in Mathematical Physics
paper · doi:10.1139/cjp-2026-0130
crossref issued 2026/01/01 · crossref published 2026/01/01 · crossref published-print 2026/01/01 · openalex publication_date 2026/06/26 · crossref created 2026/06/26 · openalex created_date 2026/06/27 · openalex updated_date 2026/07/28 · crossref deposited 2026/07/31 · crossref indexed 2026/07/31
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.