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Title: Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

We study the continuity of an abstract generalization of the maximum-entropy inference—a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for 3 × 3 matrices.
Authors:
 [1] ;  [1] ;  [2] ; ;  [3]
  1. Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795 (United States)
  2. (United Arab Emirates)
  3. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig (Germany)
Publication Date:
OSTI Identifier:
22479611
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; ENTROPY; FUNCTIONS; GEOMETRY; MAPS; MATRICES