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MiS Preprint

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

Leiba Rodman, Ilya M. Spitkovsky, Arleta Szkola and Stephan Weis


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.

Feb 26, 2015
Feb 27, 2015
MSC Codes:
81P16, 62F30, 52A20, 54C10, 62H20, 47A12, 52A10
maximum-entropy inference, quantum inference, continuity, convex body, irreducible many-party correlation, Quantum correlation, numerical range

Related publications

2016 Repository Open Access
Leiba Rodman, Ilya M. Spitkovsky, Arleta Szkoła and Stephan Weis

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

In: Journal of mathematical physics, 57 (2016), p. 1