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Entanglement measures and purification procedures
Open accessAbstract
We improve previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the quantum relative entropy and Bures metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin-1/2 systems using the quantum relative entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a number of properties of our entanglement measure that have important physical implications. We briefly explain the statistical basis of our measure of entanglement in the case of the quantum relative entropy. We then argue that our entanglement measure determines an upper bound to the number of singlets that can be obtained by any purification procedure.
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“Another quantifier of quantum correlations in such states is the so called relative entropy [6] defined as the 'distance' between the density matrix ρ and the density matrix σ of the closest disentangled state”
From Biphoton ququarts as either pure or mixed states, features and reconstruction from coincidence measurements (2013) · cites this paper as [6]
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Metadata
- Authors
- Vedral, V., & Plenio, M. B.
- Affiliations
- Imperial College London (GB)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1998-03-01
- Volume
- 57
- Issue
- 3
- Pages
- 1619-1633
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2025236523
- Cited by
- 1,419
- References
- 34
- Citations by year
- 2026: 27 · 2025: 49 · 2024: 38 · 2023: 76 · 2022: 51 · 2021: 42 · 2020: 44 · 2019: 60 · 2018: 58 · 2017: 57 · 2016: 45 · 2015: 54 · 2014: 42 · 2013: 39 · 2012: 47
- FWCI
- 55.54
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Spiral (Imperial College London) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Alexander von Humboldt-Stiftung
- 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
- entanglement measures, purification procedure, quantum relative entropy, Bures metric, singlets, entanglement quantification
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