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: 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