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Logarithmic Negativity: A Full Entanglement Monotone That is not Convex

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Plenio, M. B.·2005·Physical Review Letters

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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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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: bronze
doi.org
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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › 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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Logarithmic Negativity: A Full Entanglement Monotone That is not Convex

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