We consider the problem of the stability (with sharp exponent) of the Lieb--Solovej inequality for symmetric $SU(N)$ 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 $\mathbb{C}^d$ , for some suitable $d$ , and on some explicit (and somewhat surprising) computations.We consider the problem of the stability (with sharp exponent) of the Lieb--Solovej inequality for symmetric $SU(N)$ 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 $\mathbb{C}^d$, for some suitable $d$, and on some explicit (and somewhat surprising) computations.

math-phCross-listedarXiv:2512.04245Dec 5, 20250 citations

Proof of an entropy conjecture of Wehrl

Élliott H. Lieb

Communications in Mathematical PhysicsAug 1, 1978336 citations

Remarks on the relation between quantum and classical entropy as proposed by A. Wehrl

Armin Uhlmann

Reports on Mathematical PhysicsOct 1, 19804 citations

Wehrl entropy, Lieb conjecture, and entanglement monotones

Florian Mintert, Karol Życzkowski

We propose to quantify the entanglement of pure states of $N\ifmmode\times\else\texttimes\fi{}N$ bipartite quantum systems by defining its Husimi distribution with respect to $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(N)$ coherent states. The Wehrl entropy is minimal if and only if the analyzed pure state is separable. The excess of the Wehrl entropy is shown to be equal to the subentropy of the mixed state obtained by partial trace of the bipartite pure state. This quantity, as well as the generalized (R\'enyi) subentropies, are proved to be Schur concave, so they are entanglement monotones and may be used as alternative measures of entanglement.We propose to quantify the entanglement of pure states of $N\ifmmode\times\else\texttimes\fi{}N$ bipartite quantum systems by defining its Husimi distribution with respect to $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(N)$ coherent states. The Wehrl entropy is minimal if and only if the analyzed pure state is separable. The excess of the Wehrl entropy is shown to be equal to the subentropy of the mixed state obtained by partial trace of the bipartite pure state. This quantity, as well as the generalized (R\'enyi) subentropies, are proved to be Schur concave, so they are entanglement monotones and may be used as alternative measures of entanglement.

arXiv:quant-ph/0307169Physical Review AFeb 24, 200443 citations

Proof of the Wehrl-type Entropy Conjecture for Symmetric

{SU(N)}

Coherent States

We consider the problem of the stability (with sharp exponent) of the Lieb--Solovej inequality for symmetric

SU(N)

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

\mathbb{C}^d

, for some suitable

d

, and on some explicit (and somewhat surprising) computations.