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Cited by 353

The DOI matches its Crossref record; 138 of the 138 references it cites were found in a registry or an index.

Concepts of quantum non-Markovianity: A hierarchy

Open access
Li, Li, Hall, Michael J.W., Wiseman, Howard M.·2018·Physics Reports
DOI 10.1016/j.physrep.2018.07.001
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Abstract

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.

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Metadata

Authors
Li, L., Hall, M. J. W., & Wiseman, H. M.
Venue
Physics Reports
Publisher
Elsevier BV
Published
2018-10
Volume
759
Pages
1-51
ISSN
0370-1573 (ISSN-L)
DOI
10.1016/j.physrep.2018.07.001
OpenAlex
W2781250181
Cited by
353
References
138
FWCI
16.71
Type
journal article
Language
en
Open access
green

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