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

Tropp, Joel

doi:10.1090/S0002-9939-2011-11141-9

From joint convexity of quantum relative entropy to a concavity theorem of Lieb
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Proc. Amer. Math. Soc. 140 (2012), 1757-1760 Request permission

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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