### 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 language | English (US) |
---|---|

Number of pages | 1 |

Journal | Journal of Mathematical Physics |

Volume | 57 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2016 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*57*(1). https://doi.org/10.1063/1.4926965

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 57, no. 1. https://doi.org/10.1063/1.4926965

}

TY - JOUR

T1 - Continuity of the maximum-entropy inference

T2 - Convex geometry and numerical ranges approach

AU - Rodman, Leiba

AU - Spitkovsky, Ilya

AU - Szkola, Arleta

AU - Weis, Stephan

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84939449364&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939449364&partnerID=8YFLogxK

U2 - 10.1063/1.4926965

DO - 10.1063/1.4926965

M3 - Article

VL - 57

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 1

ER -