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Cited by 462Quantum Mechanics and ApplicationsAdvanced Thermodynamics and Statistical MechanicsQuantum Information and Cryptography

Reduced Dynamics Need Not Be Completely Positive

Pechukas, Philip·1994·Physical Review Letters
DOI 10.1103/physrevlett.73.1060
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Abstract

The reduced dynamics of a quantum system in contact with a reservoir is generally thought to be "completely positive"; this is certainly true if product initial conditions are used to define the dynamics. We show that with correlated initial conditions it need not be so. In this case the dynamics can properly be defined only on a subset of initial system states; extension, by linearity, to all possible initial states is trivially possible, but the extension may not be physically realizable and may not even be positive, let alone completely positive.

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Crossref · 10.1103/physrevlett.73.1060

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7 of 7 references verified0 citation errors · 0 not checkable

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Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The results are applicable to a wide variety of scenarios including bounding decoherence rates, quantum speed limits in dissipative state preparation, quantum computation and simulation assisted by dissipation.

    “Our results are applicable to a wide variety of scenarios including bounding decoherence rates [40], and quantum speed limits in dissipative state preparation [41], quantum computation and simulation assisted by dissipation [42].”

    From Quantum Speed Limits in Open System Dynamics (2013) · cites this paper as [42]

  • A completely positive map can be expressed in the Kraus operator sum representation.

    “The definition of a CP map Φ CP implies that it can be expressed in the Kraus operator sum representation [3]: ρ S ( t ) = ∑ α E α ( t ) ρ S (0) E † α ( t ) = Φ CP ( t )[ ρ S (0)] .”

    From Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps (2009) · cites this paper as [3]

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Related

Authors
Pechukas, P.
Affiliations
University of Augsburg (DE)
Corresponding author
Pechukas, Philip
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
1994-08-22
Volume
73
Issue
8
Pages
1060-1062
ISSN
0031-9007 (ISSN-L)
DOI
10.1103/physrevlett.73.1060
OpenAlex
W2049844449
Cited by
462
References
7
Citations by year
2026: 10 · 2025: 25 · 2024: 21 · 2023: 20 · 2022: 15 · 2021: 29 · 2020: 18 · 2019: 15 · 2018: 19 · 2017: 24 · 2016: 22 · 2015: 16 · 2014: 21 · 2013: 20 · 2012: 24
FWCI
2.44
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
reduced dynamics, completely positive maps, open quantum systems, system-reservoir coupling, physical realizability, quantum thermodynamics

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