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arXiv · 2307.14089

The generalized Wehrl entropy bound in quantitative form

Rupert L. Frank·Fabio Nicola·Paolo Tilli
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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.

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Rupert L. Frank, Fabio Nicola, Paolo Tilli. 2023-07-26. The generalized Wehrl entropy bound in quantitative form. https://arxiv.org/abs/2307.14089

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