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

Journal Article · Fri Jan 15 00:00:00 EST 2016 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4926965· OSTI ID:22479611

Rodman, Leiba ^[1]; Szkoła, Arleta; Weis, Stephan ^[2]

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1. Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795 (United States)
2. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig (Germany)

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.

• OSTI ID: 22479611
• Journal Information: Journal of Mathematical Physics, Vol. 57, Issue 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRELATIONS
ENTROPY
FUNCTIONS
GEOMETRY
MAPS
MATRICES