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Cited by 793Quantum Information and CryptographyQuantum Mechanics and ApplicationsQuantum many-body systems

An introduction to entanglement measures

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Plenio, M.B., Virmani, S.·2007·Quantum Information and Computation
DOI 10.26421/qic7.1-2-1
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Abstract

We review the theory of entanglement measures, concentrating mostly on the finite dimensional two-party case. Topics covered include: single-copy and asymptotic entanglement manipulation; the entanglement of formation; the entanglement cost; the distillable entanglement; the relative entropic measures; the squashed entanglement; log-negativity; the robustness monotones; the greatest cross-norm; uniqueness and extremality theorems. Infinite dimensional systems and multi-party settings will be discussed briefly.

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Crossref · 10.26421/qic7.1-2-1

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  • Both the robustness and the relative entropy measure are monotones under NR, convex, and faithful (zero iff ρ∈F_m).

    “Both the robustness and the relative entropy measure are monotones under NR . They are also both convex and faithful (see e.g. [4, 5]) in the sense that they are zero iff ρ ∈ F m .”

    From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [4]

  • Any measure M defined as the distance from F_m using a contractive metric C is a resource quantifier and is non-increasing under any map in NR_m.

    “where C is a contractive metric, is a resource quantifier and in particular non-increasing under any map in NR m (see e.g. [4, 5]).”

    From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [4]

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Related

Authors
Plenio, M. B., & Virmani, S.
Affiliations
Imperial College London (GB)
ORCID
Venue
Quantum Information and Computation
Publisher
Rinton Press
Published
2007-01
Volume
7
Issue
1&2
Pages
1-51
ISSN
1533-7146 (ISSN-L)
DOI
10.26421/qic7.1-2-1
OpenAlex
W2951432180
Cited by
756
References
3
Citations by year
2026: 33 · 2025: 50 · 2024: 52 · 2023: 73 · 2022: 45 · 2021: 35 · 2020: 31 · 2019: 46 · 2018: 37 · 2017: 31 · 2016: 26 · 2015: 28 · 2014: 35 · 2013: 25 · 2012: 30
FWCI
55.63
Type
journal article
Language
en
Open access
Locations
  • Quantum Information and Computation (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Leverhulme Trust
  • Engineering and Physical Sciences Research Council (GR/S82176/0)
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
entanglement measures, entanglement theory, entanglement of formation, entanglement cost, distillable entanglement, relative entropy of entanglement, squashed entanglement, entanglement robustness, uniqueness theorem, entanglement manipulation, distributed parameter systems, multipartite entanglement

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