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The generalized Wehrl entropy bound in quantitative form

  • Rupert L. Frank

    Ludwig-Maximilians-Universität München, Germany; Munich Center for Quantum Science and Technology, Germany; California Institute of Technology, Pasadena, USA
    ORCID

  • Fabio Nicola

    Politecnico di Torino, Italy

  • Paolo Tilli

    Politecnico di Torino, Italy
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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.

Cite this article

Rupert L. Frank, Fabio Nicola, Paolo Tilli, The generalized Wehrl entropy bound in quantitative form. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1674