A comparative study of relative entropy of entanglement, concurrence and negativity
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The problem of ordering of two-qubit states imposed by the relative entropy of entanglement ( E ) in comparison with the concurrence ( C ) and negativity ( N ) is studied. Analytical examples of states consistently and inconsistently ordered by the entanglement measures are given. In particular, the states for which any of the three measures imposes order opposite to that given by the other two measures are described. Moreover, examples are given of pairs of the states for which (i) and but is different from , (ii) and but differs from , (iii) , and ; and (iv) states having the same E , C and N but still violating the Bell–Clauser–Horne–Shimony–Holt inequality to different degrees.
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For an arbitrary two-qubit pure state, the Bell nonlocality measure B is equal to the negativity and concurrence, and also to the steering measure S and the fully entangled fraction.
“On the other hand, B is equal to the negativity and concurrence37,66, but also to the steering measure S and the FEF:24for an arbitrary two-qubit pure state , where a, b, c, d are the normalized complex amplitudes.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [37]
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Martínez, J. M. M. (2026) · Physics Letters A · doi:10.1016/j.physleta.2026.132041
Stronger hierarchy between local quantum uncertainty and local quantum fisher information potentials
Tian, Q., & Guo, Y.-N. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05349-0
- Authors
- Miranowicz, A., & Grudka, A.
- Affiliations
- Adam Mickiewicz University in Poznań (PL)
- Venue
- Journal of Optics B: Quantum and Semiclassical Optics
- Publisher
- IOP Publishing
- Published
- 2004-10-30
- Volume
- 6
- Issue
- 12
- Pages
- 542-548
- ISSN
- 1464-4266 (ISSN-L)
- 1741-3575
- OpenAlex
- W2151328270
- Cited by
- 86
- References
- 37
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 6 · 2023: 5 · 2022: 2 · 2021: 5 · 2020: 3 · 2019: 1 · 2018: 8 · 2017: 2 · 2016: 7 · 2015: 9 · 2014: 10 · 2013: 4 · 2012: 5
- FWCI
- 1.35
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Optics B Quantum and Semiclassical Optics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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
- relative entropy of entanglement, concurrence, negativity, two-qubit states, entanglement measures, entanglement quantification
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