On the Wehrl entropy lower bound for a locally compact abelian group

TL;DR

This paper introduces a Wehrl entropy framework for any locally compact abelian group, establishing a non-negative integer lower bound invariant and identifying coherent states as entropy minimizers.

Contribution

It generalizes Wehrl entropy to arbitrary locally compact abelian groups and proves a fundamental lower bound invariant.

Findings

Wehrl entropy is bounded below by a non-negative integer.

The minimum entropy is achieved on coherent states.

The lower bound is an invariant of the group.

Abstract

A Wehrl entropy construction is proposed for an arbitrary locally compact abelian group $G$. It is proved that the Wehrl entropy is not less than a non-negative integer, which is an invariant of the group $G$. The minimum of the Wehrl entropy is achieved on coherent states.