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arXiv:1405.7885 · Letters in Mathematical Physics

On the Joint Convexity of the Bregman Divergence of Matrices

József Pitrik, Dániel Virosztek

Published Mar 23, 2015• 24 citations
arXivHTMLPDF
DOI
10.1007/s11005-015-0757-y

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The notion of Bregman divergence and sufficiency will be defined on general convex state spaces. It is demonstrated that only spectral sets can have a Bregman divergence that satisfies a sufficiency condition. Positive elements with trace 1 in a Jordan algebra are examples of spectral sets, and the most important example is the set of density matrices with complex entries. It is conjectured that information theoretic considerations lead directly to the notion of Jordan algebra under some regularity conditions.