Quantum non-Markovianity: characterization, quantification and detection

By 'Angel Rivas, Susana F. Huelga, Martin Bodo Plenio. Reports on progress in physics. Physical Society, 2014

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We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e26ce9e5754399e0a1752aedeb6663b48376f572

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Citations in the corpus

Colloquium: Non-Markovian dynamics in open quantum systems (2015, background): “For a review on recent results on quantum non-Markovianity see Rivas et al. (2014).”
Quantum resource theories (2018, background): “…(Bartlett et al., 2007), quantum thermodynamics (Goold et al., 2016; Gour et al., 2015b), coherence (Streltsov et al., 2016), nonlocality (Brunner et al., 2014), non-Gaussianity (Weedbrook et al., 2012a), non-Markovianity (Rivas et al., 2014), and quantum correlations (Modi et al., 2012)).”
Dynamics of non-Markovian open quantum systems (2015, methodology): “Based on this, and on their conceptual basis, these non-Markovianity measures can be classified in different ways [see for instance (Rivas et al., 2014) and (Hall et al., 2014)].”
Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “Progress has been made in characterising non-Markovianity [492] in particular by analysing information backflow and structured environmental spectral densities [94], and a hierarchy for abundant definitions of (non)Markovianity has been set up [381].”