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 Full-text PDF
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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Joel A. Tropp Affiliation:
Department of Computing and Mathematical Sciences, California Institute of Technology, 1200 E. California Boulevard, MC 305-16, Pasadena, California 91125