Maximum-entropy inference and inverse continuity of the numerical range
Mathematical Physics
2016-05-17 v2 math.MP
Quantum Physics
Abstract
We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the set-valued inverse numerical range map. This gives a continuity condition in terms of analytic eigenvalue functions which implies that discontinuities are very rare. It shows also that the continuity of the MaxEnt inference method is independent of the prior state.
Keywords
Cite
@article{arxiv.1502.03970,
title = {Maximum-entropy inference and inverse continuity of the numerical range},
author = {Stephan Weis},
journal= {arXiv preprint arXiv:1502.03970},
year = {2016}
}
Comments
15 pages, no figures, correction of v1 in Coro. 5.1 and Thm. 5.3