An entropic uncertainty principle for positive operator valued measures
Functional Analysis
2012-05-29 v2 Mathematical Physics
math.MP
Abstract
Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields spatial-spectral uncertainty principles and log-Sobolev inequalities for invariant operators on homogeneous spaces, which are sharp in the compact case.
Cite
@article{arxiv.1109.5889,
title = {An entropic uncertainty principle for positive operator valued measures},
author = {Michel Rumin},
journal= {arXiv preprint arXiv:1109.5889},
year = {2012}
}
Comments
14 pages. v2: a technical assumption removed in main result