From joint convexity of quantum relative entropy to a concavity theorem of Lieb
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- by Joel A. Tropp PDF
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Abstract:
This paper provides a succinct proof of a 1973 theorem of Lieb that establishes the concavity of a certain trace function. The development relies on a deep result from quantum information theory, the joint convexity of quantum relative entropy, as well as a recent argument due to Carlen and Lieb.References
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Additional Information
- Joel A. Tropp
- Affiliation: Department of Computing and Mathematical Sciences, California Institute of Technology, 1200 E. California Boulevard, MC 305-16, Pasadena, California 91125
- Received by editor(s): January 2, 2011
- Received by editor(s) in revised form: January 4, 2011
- Published electronically: August 4, 2011
- Communicated by: Marius Junge
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 1757-1760
- MSC (2010): Primary 52A41
- DOI: https://doi.org/10.1090/S0002-9939-2011-11141-9
- MathSciNet review: 2869160