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Proceedings of the London Mathematical Society

An elementary approach to Wehrl‐type entropy bounds in quantitative form

Fabio Nicola, Federico Riccardi, Paolo Tilli

Published Jul 1, 2026• 0 citations
Publisher

Abstract

Abstract We consider the problem of the stability (with sharp exponent) of the Lieb–Solovej inequality for symmetric coherent states, which was obtained only recently by the authors. Here, we propose an elementary proof of this result, based on reformulating the Wehrl‐type entropy as a function defined on the unit sphere in , for some suitable , and on some explicit (and somewhat surprising) computations.

DOI
10.1112/plms.70182

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Abstract We consider the problem of the stability (with sharp exponent) of the Lieb–Solovej inequality for symmetric coherent states, which was obtained only recently by the authors. Here, we propose an elementary proof of this result, based on reformulating the Wehrl‐type entropy as a function defined on the unit sphere in , for some suitable , and on some explicit (and somewhat surprising) computations.
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Proof of the Wehrl-type Entropy Conjecture for Symmetric SU(N){SU(N)}SU(N) Coherent States
Abstract. We generalize the concept of the Wehrl entropy of quantum states which gives a basis–independent measure of their localization in phase space. We discuss the minimal values and the typical values of these Rényi–Wehrl entropies for pure states for spin systems. According to Lieb’s conjecture the minimal values are provided by the spin coherent states. Though Lieb’s conjecture remains unproven, we give new proofs of partial results that may be generalized for other systems. We also investigate random pure states and calculate the mean Rényi–Wehrl entropies averaged over the natural measure in the space of pure quantum states. 1.