Entropy distance: New quantum phenomena

Journal Article · Mon Oct 15 00:00:00 EDT 2012 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4757652· OSTI ID:22093758

Weis, Stephan ^[1]; Knauf, Andreas ^[2]

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1. Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig (Germany)
2. Department of Mathematics, Friedrich-Alexander-University Erlangen-Nuremberg, Cauerstr. 11, D-91058 Erlangen (Germany)

We study a curve of Gibbsian families of complex 3 Multiplication-Sign 3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance, and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology, and information geometry. This research is motivated by a theory of infomax principles, where we contribute by computing first order optimality conditions of the entropy distance.

• OSTI ID: 22093758
• Journal Information: Journal of Mathematical Physics, Vol. 53, Issue 10; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

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