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Cited by 1,530Quantum Information and CryptographyQuantum Mechanics and ApplicationsQuantum many-body systems

Logarithmic Negativity: A Full Entanglement Monotone That is not Convex

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Plenio, M. B.·2005·Physical Review Letters
DOI 10.1103/physrevlett.95.090503
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Abstract

It is proven that logarithmic negativity does not increase on average under a general positive partial transpose preserving operation (a set of operations that incorporate local operations and classical communication as a subset) and, in the process, a further proof is provided that the negativity does not increase on average under the same set of operations. Given that the logarithmic negativity is not a convex function this result is surprising, as it is generally considered that convexity describes the local physical process of losing information. The role of convexity and, in particular, its relation (or lack thereof) to physical processes is discussed and importance of continuity in this context is stressed.

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Crossref · 10.1103/physrevlett.95.090503

Cites

46 of 46 references verified0 citation errors · 0 not checkable

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  • The state (140) belongs to the class of X-states, for which the optimization problem in equation (152) can be efficiently solved.

    “For the quantum discord, note that the state (140) belongs to the subclass known as 'X-states', for which the optimization problem in equation ( 152) can be efficiently solved [230,245].”

    From Quantum non-Markovianity: characterization, quantification and detection (2014) · cites this paper as [245]

    The paper’s Abstract discusses entanglement measures and the difficulty of optimizing some of them, but not quantum discord. Searches for quantum discord and X-states found no passage identifying the citing paper’s state (140) as an X-state or addressing efficient solution of its equation (152). (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • In the pure dephasing model, the quantum discord equals Q E(t,0).

    “D Q A [ρ SA (t)] = Q E (t,0) ,(158)”

    From Quantum non-Markovianity: characterization, quantification and detection (2014) · cites this paper as [245]

    The paper’s discussion of entanglement monotones and logarithmic negativity (Abstract; Notations and definitions, page unavailable) does not address the stated equality. Searches for quantum discord and the pure dephasing model found no passage in our copy supporting it. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

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Cites

Flagged first, then by citations

Research works printed but not linked: 34

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Authors
Plenio, M. B.
Affiliations
Imperial College London (GB)
Corresponding author
Plenio, M. B.
ORCID
Plenio, M. B.
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2005-08-26
Volume
95
Issue
9
Pages
090503-090503
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.95.090503
OpenAlex
W1979369481
Semantic Scholar
64435b0cfa00fafcfdca6d566eaca7dd6a824169
Cited by
1,530
References
42
Citations by year
2026: 107 · 2025: 187 · 2024: 148 · 2023: 172 · 2022: 144 · 2021: 78 · 2020: 86 · 2019: 76 · 2018: 68 · 2017: 63 · 2016: 70 · 2015: 65 · 2014: 45 · 2013: 32 · 2012: 28
FWCI
25.35
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • PubMed (publishedVersion)
  • Spiral (Imperial College London) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Leverhulme Trust
  • Engineering and Physical Sciences Research Council
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • 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 many-body systems
Keywords
logarithmic negativity, entanglement monotones, non-convexity, positive partial transpose, local operations and classical communication, quantum entanglement, information loss

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