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Logarithmic Negativity: A Full Entanglement Monotone That is not Convex
Open accessAbstract
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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“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]
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“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]
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Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118
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Metadata
- 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
- 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
- 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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