Published May 2012
| Submitted + Published
Journal Article
Open
From joint convexity of quantum relative entropy to a concavity theorem of Lieb
- Creators
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Tropp, Joel A.
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.
Additional Information
© 2012 American Mathematical Society. Received by the editors January 2, 2011 and, in revised form, January 4, 2011. The author thanks Eric Carlen for a very illuminating discussion of matrix convexity theorems, including the paper [CL08], as well as comments on an early draft of this paper. Edward Effros contributed insights on quantum information theory, and Elliott Lieb emphasized the equivalences among concavity theorems. This work has been supported in part by ONR awards N00014-08-1-0883 and N00014-11-1-0025, AFOSR award FA9550-09-1-0643, and a Sloan Fellowship. The research was performed while the author attended the IPAM Fall 2010 program on optimization.Attached Files
Published - Tropp2012p18146P_Am_Math_Soc.pdf
Submitted - 1101.1070.pdf
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Tropp2012p18146P_Am_Math_Soc.pdf
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Additional details
- Eprint ID
- 31462
- Resolver ID
- CaltechAUTHORS:20120515-094709707
- N00014-08-1-0883
- Office of Naval Research (ONR)
- N00014-11-1- 0025
- Office of Naval Research (ONR)
- FA9550-09-1-0643
- Air Force Office of Scientific Research (AFOSR)
- Alfred P. Sloan Foundation
- Created
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2012-05-15Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field