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Cited by 448Quantum Mechanics and ApplicationsQuantum Information and CryptographyAdvanced Thermodynamics and Statistical Mechanics

The DOI matches its Crossref record; 117 of the 117 references it cites were found in a registry or an index.

Symmetries and conserved quantities in Lindblad master equations

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Albert, Victor V., Jiang, Liang·2014·Physical Review A
DOI 10.1103/physreva.89.022118
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Abstract

This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations of unitary quantum mechanics, extending the intuition of symmetries and conserved quantities to the dissipative case. We combine and apply various results to obtain an exhaustive characterization of the infinite-time behavior of Lindblad evolution, including both the structure of the infinite-time density matrix and its dependence on initial conditions. The effect of the environment in the infinite-time limit can therefore be tracked exactly for arbitrary state initialization and without knowledge of dynamics at intermediate time. As a consequence, sufficient criteria for determining the steady state of a Lindblad master equation are obtained. These criteria are knowledge of the initial state, a basis for the steady-state subspace, and all conserved quantities. We give examples of two-qubit dissipation and single-mode $d$-photon absorption where all quantities are determined analytically. Applications of these techniques to quantum information, computation, and feedback control are discussed.

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  1. M. Petkovsek, 1997, A=B

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Metadata

Authors
Albert, V. V., & Jiang, L.
Affiliations
Yale University (US)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2014-02-21
Volume
89
Issue
2
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.89.022118
OpenAlex
W2044042033
Cited by
448
References
117
Citations by year
2026: 56 · 2025: 72 · 2024: 60 · 2023: 44 · 2022: 43 · 2021: 39 · 2020: 49 · 2019: 29 · 2018: 19 · 2017: 11 · 2016: 12 · 2015: 8 · 2014: 6
FWCI
6.14
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Keywords
Lindblad master equation, steady state, first integrals, quantum symmetries, dissipative quantum systems, quantum feedback control, quantum information

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