On the existence of quantum subdynamics
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It is shown, using only elementary operator algebra, that an open quantum system coupled to its environment will have a subdynamics (reduced dynamics) as an exact consequence of the reversible dynamics of the composite system only when the states of system and environment are uncorrelated. Furthermore, it is proved that for a finite temperature the KMS condition for the lowest-order correlation function cannot be reproduced by any type of linear subdynamics except the reversible Hamiltonian one of a closed system. The first statement can be seen as a particular case of a more general theorem of Takesaki on the properties of conditional expectations in von Neumann algebras. The concept of subdynamics used here allows for memory effects, no assumption is made of a Markov property. For dynamical systems based on commutative algebras of observables the subdynamics always exists as a stochastic process in the random variable defining the open subsystem.
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The problem of identifying the general physical conditions under which completely positive maps are valid had remained open since it was first posed.
“For this reason it is perhaps surprising that the problem of identifying the general physical conditions under which CP maps are valid has remained open since it was first posed in a vigorous debate [5, 6].”
From Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps (2009) · cites this paper as [5]
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Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps
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- Authors
- Lindblad, G.
- Affiliations
- KTH Royal Institute of Technology (SE)
- Corresponding author
- Lindblad, Göran
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1996-07-21
- Volume
- 29
- Issue
- 14
- Pages
- 4197-4207
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2076708974
- Cited by
- 41
- References
- 25
- Citations by year
- 2022: 1 · 2021: 2 · 2020: 1 · 2018: 3 · 2016: 1 · 2015: 2 · 2013: 4 · 2012: 1
- FWCI
- 0.24
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- reduced dynamics, open quantum systems, system-environment coupling, conditional expectation, von Neumann algebras, KMS condition, correlation functions, memory effects, non-Markovian dynamics, finite temperature, stochastic processes
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