Concepts of quantum non-Markovianity: A hierarchy
By Li Li, Michael J. W. Hall, Howard M. Wiseman. Physics reports, 2017
371 citations recorded by the source corpus.
Markovian approximation is a widely-employed idea in descriptions of the dynamics of open quantum systems (OQSs). Although it is usually claimed to be a concept inspired by classical Markovianity, the term quantum Markovianity is used inconsistently and often unrigorously in the literature. In this report we compare the descriptions of classical stochastic processes and quantum stochastic processes (as arising in OQSs), and show that there are inherent differences that lead to the non-trivial problem of characterizing quantum non-Markovianity. Rather than proposing a single definition of quantum Markovianity, we study a host of Markov-related concepts in the quantum regime. Some of these concepts have long been used in quantum theory, such as quantum white noise, factorization approximation, divisibility, Lindblad master equation, etc.. Others are first proposed in this report, including those we call past-future independence, no (quantum) information backflow, and composability. All of these concepts are defined under a unified framework, which allows us to rigorously build hierarchy relations among them. With various examples, we argue that the current most often used definitions of quantum Markovianity in the literature do not fully capture the memoryless property of OQSs. In fact, quantum non-Markovianity is highly context-dependent. The results in this report, summarized as a hierarchy figure, bring clarity to the nature of quantum non-Markovianity.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/eaf67258473973fc181d97436a892f7dd6c6482e
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In Atomic and Molecular Physics, and Optics
- Thomas Schulte-Herbrüggen
- Ronnie Kosloff
- Simone Montangero
- Dominique Sugny
- Tommaso Calarco
- Christiane P. Koch
- Frank K. Wilhelm
- Steffen J. Glaser
Citations in the corpus
- Detecting crosstalk errors in quantum information processors (2019, neutral): “[12, 8, 59, 3, 32, 60].”
- 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].”