A schwarz inequality for positive linear maps on $C^{\ast}$-algebras
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This behavior was first observed by Fuchs for a non-extreme channel, and the amplitude-damping channel was later studied by Schumacher and Westmoreland.
“This behavior was observed first by Fuchs for a non-extreme channel [5]; subsequently, the amplitude-damping channel was studied by Schumacher and Westmoreland [23].”
From An analysis of completely-positive trace-preserving maps on M2 (2002) · cites this paper as [5]
In both cited cases the work was numerical, but it suggests that this situation is generic for channels translated orthogonal to the major axis of the ellipse.
“In both cases the work was numerical, but suggests that this situation is generic for channels that are translated orthogonal to the major axis of the ellipse.”
From An analysis of completely-positive trace-preserving maps on M2 (2002) · cites this paper as [5]
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Cites
Positive Functions on C ∗ -Algebras
Stinespring, W. F. (1955) · Proceedings of the American Mathematical Society · doi:10.2307/2032342 · Cited by 753 · see citing works
Isometries of Operator Algebras
Kadison, R. V. (1951) · Annals of Mathematics · doi:10.2307/1969534 · Cited by 565 · see citing works
Positive linear maps of operator algebras
Størmer, E. (1963) · Acta Mathematica · doi:10.1007/bf02391860 · Cited by 354 · see citing works
Kadison, R. V., & Singer, I. M. (1959) · American Journal of Mathematics · doi:10.2307/2372748 · Cited by 231 · see citing works
A Schwarz inequality for convex operator functions
Davis, C. (1957) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1957-0084120-4 · Cited by 150 · see citing works
All convex invariant functions of hermitian matrices
Davis, C. (1957) · Archiv der Mathematik · doi:10.1007/bf01898787 · Cited by 120 · see citing works
On the Jordan Structure of C ∗ -Algebras
Størmer, E. (1965) · Transactions of the American Mathematical Society · doi:10.2307/1994536 · Cited by 102 · see citing works
Notions generalizing convexity for functions defined on spaces of matrices
Davis, C. (1963) · Proceedings of symposia in pure mathematics · doi:10.1090/pspum/007/0155837 · Cited by 68 · see citing works
Positive definite function and direct product Hilbert space
Umegaki, H. (1955) · Tohoku Mathematical Journal · doi:10.2748/tmj/1178245059 · Cited by 24 · see citing works
Operator-valued entropy of a quantum mechanical measurement
Davis, C. (1961) · Proceedings of the Japan Academy Series A Mathematical Sciences · doi:10.3792/pja/1195523583 · Cited by 23 · see citing works
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Research works printed but not linked: 8
- W. B. ARVESON, Subalgebras of C*-algebras I, Acta Math., vol. 123 (1969), pp. 141- 2.
- Subalgebras of C*-algebras H, Acta Math., vol. 128 (1972), pp. 271-308.
- J. BN SD S. SHN, Monotone and convex opera,or functions, Trans. Amer. Math. Soc., vol. 79 (1955), pp. 58-71.
- M. D. CHO, Positive linear maps on C*-algebr, Canad. J. Math., vol. 24 (1972), pp. 52529.
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- A generalized Schwarz inequality and algebraic invariants for operator algebra, Ann. of Math., vol. 56 (1952), pp. 494-503.
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- H. UMEGAKI, Positive definitefunction and direct product Hilbert space, TShoku Math. J. (2), vol. 7 (1955), pp. 206-211.
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Finitely correlated states on quantum spin chains
Fannes, M., Nachtergaele, B., & Werner, R. F. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02099178 · Cited by 1,422 · see citing works
Properties of quantum Markovian master equations
Gorini, V., Frigerio, A., Verri, M., Kossakowski, A., & Sudarshan, E. C. G. (1978) · Reports on Mathematical Physics · doi:10.1016/0034-4877(78)90050-2 · Cited by 468 · see citing works
An analysis of completely-positive trace-preserving maps on M2
Beth Ruskai, M., Szarek, S., & Werner, E. (2002) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(01)00547-x · Cited by 366 · see citing works
Affine maps of density matrices
Jordan, T. F. (2005) · Physical Review A · doi:10.1103/physreva.71.034101 · Cited by 17 · see citing works
- Authors
- Choi, M.-D.
- Affiliations
- University of Toronto (CA)
- Corresponding author
- Choi, Man-Duen
- Venue
- Illinois Journal of Mathematics
- Publisher
- Duke University Press
- Published
- 1974-12-01
- Volume
- 18
- Issue
- 4
- Pages
- 565-574
- ISSN
- 0019-2082 (ISSN-L)
- 1945-6581
- OpenAlex
- W1481217622
- Cited by
- 295
- References
- 10
- Citations by year
- 2026: 5 · 2025: 13 · 2024: 14 · 2023: 14 · 2022: 10 · 2021: 13 · 2020: 40 · 2019: 9 · 2018: 14 · 2017: 10 · 2016: 14 · 2015: 12 · 2014: 7 · 2013: 7 · 2012: 5
- FWCI
- 1.89
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Illinois Journal of Mathematics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Inequalities and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Keywords
- Cauchy-Schwarz inequality, positive linear maps, C*-algebras, operator algebras
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