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

Leiba Rodman, Ilya Spitkovsky, Arleta Szkola, Stephan Weis

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Number of pages1
JournalJournal of Mathematical Physics
Volume57
Issue number1
DOIs
StatePublished - Jan 1 2016

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Extremal Point
Convex Geometry
Numerical Range
Linear map
Maximum Entropy
Convex Body
inference
continuity
Discontinuity
discontinuity
entropy
geometry
Continuous Function
Maximise
Fiber
fibers
matrices
Generalization

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Continuity of the maximum-entropy inference : Convex geometry and numerical ranges approach. / Rodman, Leiba; Spitkovsky, Ilya; Szkola, Arleta; Weis, Stephan.

In: Journal of Mathematical Physics, Vol. 57, No. 1, 01.01.2016.

Research output: Contribution to journalArticle

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