TY - JOUR

T1 - Concepts of quantum non-Markovianity

T2 - A hierarchy

AU - Li, Li

AU - Hall, Michael J.W.

AU - Wiseman, Howard M.

N1 - Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2018/10/18

Y1 - 2018/10/18

N2 - 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, and GKS–Lindblad master equation. 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.

AB - 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, and GKS–Lindblad master equation. 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.

KW - Open quantum systems

KW - Quantum Markovianity

KW - Quantum control

KW - Quantum measurement

KW - Quantum non-Markovianity

UR - http://www.scopus.com/inward/record.url?scp=85050821970&partnerID=8YFLogxK

U2 - 10.1016/j.physrep.2018.07.001

DO - 10.1016/j.physrep.2018.07.001

M3 - Review article

SN - 0370-1573

VL - 759

SP - 1

EP - 51

JO - Physics Reports

JF - Physics Reports

ER -