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The generalized Wehrl entropy bound in quantitative form
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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.
Forward citations
Cited by 3 Pith papers
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On the existence of extremizers for the sum of eigenvalues of Toeplitz operators
For every k and every prescribed measure, the supremum of the sum of the first k Toeplitz eigenvalues is attained, in the Fock space and in a general wavelet setting.
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Wehrl inequalities for matrix coefficients of holomorphic discrete series
Sharp L^2-L^{2n} Wehrl inequalities hold for matrix coefficients of vector-valued holomorphic discrete series, with maximizers exactly the reproducing kernels.
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Optimal transport maps, majorization, and log-subharmonic measures
A trace-level analogue of Caffarelli's contraction theorem is proved for log-subharmonic sources, yielding majorization, entropy stability, and new proofs of Wehrl-type inequalities.
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