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Cited by 54Quantum Mechanics and ApplicationsQuantum Information and CryptographyAdvanced Thermodynamics and Statistical Mechanics

Markovianity criteria for quantum evolution

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Chruściński, Dariusz, Kossakowski, Andrzej·2012·Journal of Physics B: Atomic, Molecular and Optical Physics
DOI 10.1088/0953-4075/45/15/154002
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Abstract

We characterize a class of Markovian dynamics using the concept of a divisible dynamical map. Moreover, we provide a family of criteria which can distinguish Markovian and non-Markovian dynamics. These Markovianity criteria are based on a simple observation that Markovian dynamics implies monotonic behaviour of several well-known quantities such as distinguishability of states, fidelity, relative entropy and genuine entanglement measures.

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  • An operator is the generator of a quantum Markov or divisible process exactly when it can be written in the Gorini-Kossakowski-Susarshan-Lindblad form with nonnegative coefficients.

    “Theorem 3.1 (Gorini-Kossakowski-Susarshan-Lindblad). An operator L t is the generator of a quantum Markov (or divisible) process if and only if it can be written in the form dρ(t) dt = L t [ρ(t)] = -i[H (t), ρ(t)] + k γ k (t) V k (t)ρ(t)V † k (t) - 1 2 {V † k (t)V k (t), ρ(t)} , (32 ) where H (t) and V k (t) are time-dependent operators, with H (t) self-adjoint, and γ k (t) 0 for every k and time”

    From Quantum non-Markovianity: characterization, quantification and detection (2014) · cites this paper as [32]

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Authors
Chruściński, D., & Kossakowski, A.
Affiliations
Nicolaus Copernicus University (PL)
Venue
Journal of Physics B: Atomic, Molecular and Optical Physics
Publisher
IOP Publishing
Published
2012-07-30
Volume
45
Issue
15
Pages
154002
ISSN
  • 0953-4075 (ISSN-L)
  • 1361-6455
DOI
10.1088/0953-4075/45/15/154002
OpenAlex
W1973479161
Semantic Scholar
858125385aef261b5267fdb8531a724ae8dd1619
Cited by
54
References
42
Citations by year
2025: 1 · 2023: 3 · 2022: 4 · 2021: 7 · 2020: 6 · 2019: 4 · 2018: 8 · 2017: 3 · 2016: 4 · 2015: 6 · 2014: 4 · 2013: 4
FWCI
2.32
Type
journal article
Language
en
Open access
Locations
  • Journal of Physics B Atomic Molecular and Optical Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Nicolaus Copernicus University Repository (Nicolaus Copernicus University) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Keywords
non-Markovian dynamics, quantum dynamical maps, quantum state distinguishability, fidelity, Kullback-Leibler divergence, open quantum systems

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