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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Continuity of the maximum-entropy inference: convex geometry and numerical ranges approach
Leiba Rodman, Ilya M. Spitkovsky, Arleta Szkola and Stephan WeisAbstract
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.
- Received:
- 26.02.15
- Published:
- 27.02.15
- MSC Codes:
- 81P16, 62F30, 52A20, 54C10, 62H20, 47A12, 52A10
- Keywords:
- maximum-entropy inference, quantum inference, continuity, convex body, irreducible many-party correlation, Quantum correlation, numerical range