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Cited by 155Quantum Mechanics and ApplicationsQuantum Information and CryptographyQuantum Computing Algorithms and Architecture

The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.

Finding the Kraus decomposition from a master equation and vice versa

Open access
Andersson, Erika, Cresser, James D., Hall, Michael J. W.·2007·Journal of Modern Optics
DOI 10.1080/09500340701352581
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Abstract

For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure is given for constructing the corresponding linear map from the initial state to the state at time t, including its Kraus-type representations. Formally, this is equivalent to solving the master equation. For an N-dimensional Hilbert space it requires (i) solving a first order N 2×N 2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalizing a related N 2×N 2 matrix (to obtain a Kraus-type representation). Conversely, for a given time-dependent linear map, a necessary and sufficient condition is given for the existence of a corresponding master equation, where the (not necessarily unique) form of this equation is explicitly determined. It is shown that a “best possible” master equation may always be defined, for approximating the evolution in the case that no exact master equation exists. Examples involving qubits are given.

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Research works printed but not linked: 3

  1. Zwanzig R, 1960, Phys., 33, 1338
  2. Breuer H-P, 2002, Petruccione, The Theory of Open Quantum Systems
  3. Aliferis P, 2006, Preskill, Quant. Inf. Comput., 6, 97

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Metadata

Authors
Andersson, E., Cresser, J. D., & Hall, M. J. W.
Affiliations
  • University of Strathclyde (GB)
  • Macquarie University (AU)
  • Australian National University (AU)
Corresponding author
Andersson, Erika
ORCID
Venue
Journal of Modern Optics
Publisher
Informa UK Limited
Published
2007-08-15
Volume
54
Issue
12
Pages
1695-1716
ISSN
  • 0950-0340 (ISSN-L)
  • 1362-3044
DOI
10.1080/09500340701352581
OpenAlex
W2140406475
Cited by
155
References
28
Citations by year
2026: 2 · 2025: 12 · 2024: 14 · 2023: 13 · 2022: 11 · 2021: 9 · 2020: 13 · 2019: 8 · 2018: 14 · 2017: 13 · 2016: 8 · 2015: 9 · 2014: 7 · 2013: 6 · 2012: 6
FWCI
1.63
Type
journal article
Language
en
Open access
Locations
  • Journal of Modern Optics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • ANU Open Research (Australian National University) (submittedVersion)
  • Griffith Research Online (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Royal Society
  • Macquarie 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 › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords
Kraus decomposition, master equation, completely positive maps, non-Markovian dynamics, quantum dynamical maps, time-local master equation, qubits, quantum state evolution

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