Discontinuities in the Maximum-Entropy Inference
Abstract
We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of discontinuities in this inference method. This is a pure quantum phenomenon since the maximum-entropy inference is continuous for mutually commuting observables. The question arises why some sets of observables are distinguished by a discontinuity in an inference method which is still discussed as a universal inference method. In this paper we make an example of a discontinuity and we explain a characterization of the discontinuities in terms of the openness of the (restricted) linear map that assigns expected values to states.
Cite
@article{arxiv.1308.6126,
title = {Discontinuities in the Maximum-Entropy Inference},
author = {Stephan Weis},
journal= {arXiv preprint arXiv:1308.6126},
year = {2016}
}
Comments
8 pages, 3 figures, 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Garching, Germany, 15-20 July 2012