On Lieb's conjecture for the Wehrl entropy of Bloch coherent states

TL;DR

This paper proves Lieb's conjecture for the Wehrl entropy of Bloch coherent states specifically for spins 1 and 3/2, and extends the analysis to arbitrary spins using geometric and group theoretic methods.

Contribution

It provides the first proofs of Lieb's conjecture for specific low spins and introduces a geometric approach to evaluate entropy integrals for all spins.

Findings

Lieb's conjecture verified for spin 1 and 3/2.

Explicit entropy calculations for spins 1, 3/2, and 2.

Group theoretic proof of a related entropy inequality for all spins.

Abstract

Lieb's conjecture for the Wehrl entropy of Bloch coherent states is proved for spin 1 and spin 3/2. Using a geometric representation we solve the entropy integrals for states of arbitrary spin and evaluate them explicitly in the cases of spin 1, 3/2, and 2. We also give a group theoretic proof for all spin of a related inequality.