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From joint convexity of quantum relative entropy to a concavity theorem of Lieb


Author: Joel A. Tropp
Journal: Proc. Amer. Math. Soc. 140 (2012), 1757-1760
MSC (2010): Primary 52A41
Published electronically: August 4, 2011
MathSciNet review: 2869160
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Abstract | References | Similar Articles | Additional Information

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.


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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

DOI: https://doi.org/10.1090/S0002-9939-2011-11141-9
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
Article copyright: © Copyright 2011 American Mathematical Society