Optimizing entropy relative to a channel or a subalgebra
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It is sufficient to consider ensembles with cardinality not larger than the square of the considered state's rank.
“There is no a priori maximum cardinality, though it is sufficient to consider ensembles with cardinality not larger than the square of the considered state's rank [52].”
From Measures and dynamics of entangled states (2005) · cites this paper as [52]
Cites
Mixed-state entanglement and quantum error correction
Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review A · doi:10.1103/physreva.54.3824 · Cited by 5,272 · see citing works
Entanglement of a pair of quantum bits
Hill, S., & Wootters, W. K. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.5022 · Cited by 2,823 · see citing works
Wehrl, A. (1978) · Reviews of Modern Physics · doi:10.1103/revmodphys.50.221 · Cited by 1,963 · see citing works
大矢, 雅., & Petz, D. (1993) · Cited by 817 · see citing works
Nutt, G. J. (1992) · Cited by 317 · see citing works
FROM RELATIVE ENTROPY TO ENTROPY
Narnhofer, H., & Thirring, W. E. (1985) · Fizika · Cited by 34 · see citing works
Optimal decompositions of quantum states with respect to entropy
Benatti, F., Narnhofer, H., & Uhlmann, A. (1996) · Reports on Mathematical Physics · doi:10.1016/0034-4877(96)87681-6 · Cited by 31 · see citing works
Entropy of a subalgebra and quantum estimation
Benatti, F. (1996) · Journal of Mathematical Physics · doi:10.1063/1.531682 · Cited by 17 · see citing works
Optimizing entropy relative to a channel or a subalgebraPreprint
Uhlmann, A. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9701014 · Cited by 16 · see citing works
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Fidelity and concurrence of conjugated states
Uhlmann, A. (2000) · Physical Review A · doi:10.1103/physreva.62.032307 · Cited by 421 · see citing works
Concurrence of mixed bipartite quantum states in arbitrary dimensions
Mintert, F., Kuś, M., & Buchleitner, A. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.167902 · Cited by 246 · see citing works
The Schmidt number as a universal entanglement measure
Sperling, J., & Vogel, W. (2011) · Physica Scripta · doi:10.1088/0031-8949/83/04/045002 · Cited by 96 · see citing works
- Authors
- Uhlmann
- Venue
- Open Systems & Information Dynamics
- Published
- 1998
- Volume
- 5
- Issue
- 3
- Pages
- 209-228
- ISSN
- 1230-1612 (ISSN-L)
- OpenAlex
- W1725167044
- Cited by
- 181
- References
- 9
- Citations by year
- 2026: 5 · 2025: 6 · 2024: 6 · 2023: 11 · 2022: 3 · 2021: 8 · 2020: 5 · 2019: 6 · 2018: 2 · 2017: 4 · 2016: 10 · 2015: 9 · 2014: 12 · 2013: 5 · 2012: 11
- FWCI
- 7.48
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Open Systems & Information Dynamics (publishedVersion)
- 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 › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Keywords
- quantum entropy, entanglement of formation, subfactors, maximal commutative subalgebras, full matrix algebras, finite-dimensional quantum systems, convexity, symmetry
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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