A lower bound for the Wehrl entropy of quantum spin with sharp high-spin asymptotics

Abstract

A lower bound for the Wehrl entropy of a single quantum spin is derived. The high-spin asymptotics of this bound coincides with Lieb's conjecture up to, but not including, terms of first and higher order in the inverse spin quantum number. The result presented here may be seen as complementary to the verification of the conjecture in cases of lowest spin by Schupp [Commun. Math. Phys. 207 (1999), 481]. The present result for the Wehrl-entropy is obtained from interpolating a sharp norm bound that also implies a sharp lower bound for the so-called R\'enyi-Wehrl entropy with certain indices that are evenly spaced by half of the inverse spin quantum number.