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

We consider the problem of the stability (with sharp exponent) of the Lieb–Solovej inequality for symmetric 𝑆⁢𝑈⁡(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 ℂ𝑑 , for some suitable 𝑑 , and on some explicit (and somewhat surprising) computations.