Information Geometry and its Applications III

Abstract Stephan Weis

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Stephan Weis  (Universität Erlangen, Germany)
Friday, August 06, 2010, room Hörsaal 1
Entropy distance: new quantum phenomena

The relative entropy distance of a state from an exponential family is important in information theory and statistics. Two-dimensional examples in the algebra of complex formula6-matrices reveal that the mean value set of an exponential family has typically non-exposed faces. The Staffelberg family stands out of these examples due to a discontinuous entropy distance.

We meet these phenomena e.g. in optimization problems on the state space (including singular states). They do not occur in the probabilistic case of an abelian formula8-subalgebra of complex formula10-matrices. Analogues of probability theory exist in the non-abelian quantum case, though: The entropy distance from an exponential family in a finite-dimensional formula12-algebra is given by a projection to an extension of the family. An optimal form of the Pythagorean theorem of relative entropy holds for this extension. We conclude with applications.

Part of this work is jointly with Andreas Knauf.

 

Date and Location

August 02 - 06, 2010
University of Leipzig
Augustusplatz
04103 Leipzig
Germany

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
Germany
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Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
Italy
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František Matúš
Academy of Sciences of the Czech Republic
Institute of Information Theory and Automation
Czech Republic
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Scientific Committee

Shun-ichi Amari
RIKEN
Brain Science Institute, Mathematical Neuroscience Laboratory
Japan
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
Hungary
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
Hungary
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
Italy
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Administrative Contact

Antje Vandenberg
Max Planck Institute for Mathematics in the Sciences
Contact by Email
Phone: (++49)-(0)341-9959-552
Fax: (++49)-(0)341-9959-555

05.04.2017, 12:42