The generalized Wehrl entropy bound in quantitative form
Mathematical Physics
2023-11-02 v3 Classical Analysis and ODEs
Complex Variables
Functional Analysis
math.MP
Abstract
Lieb and Carlen have shown that mixed states with minimal Wehrl entropy are coherent states. We prove that mixed states with almost minimal Wehrl entropy are almost coherent states. This is proved in a quantitative sense where both the norm and the exponent are optimal and the constant is explicit. We prove a similar bound for generalized Wehrl entropies. As an application, a sharp quantitative form of the log-Sobolev inequality for functions in the Fock space is provided.
Keywords
Cite
@article{arxiv.2307.14089,
title = {The generalized Wehrl entropy bound in quantitative form},
author = {Rupert L. Frank and Fabio Nicola and Paolo Tilli},
journal= {arXiv preprint arXiv:2307.14089},
year = {2023}
}
Comments
23 pages. Significantly revised to encompass density matrices as well (not only pure states)