Wehrl entropy, coherent states and quantum channels

TL;DR

This paper reviews Wehrl entropy, coherent states, and quantum channels, discussing Lieb's conjecture, its proof, and physical implications, highlighting their interconnected roles in quantum information theory.

Contribution

It provides an overview of Wehrl entropy, Lieb's conjecture, and the role of covariant quantum channels, offering new perspectives on coherent states and their physical applications.

Findings

Lieb's conjecture has been proven, confirming properties of Wehrl entropy.

Covariant quantum channels are crucial in understanding semiclassical entropy.

The paper introduces an alternative definition of coherent states with physical relevance.

Abstract

We review Wehrl's definition of a semiclassical entropy in terms of coherent states and give an introductory overview of Lieb's conjecture, its proof (including earlier results), generalizations, and the role of covariant quantum channels in this context. These structures motivate an alternative definition of coherent states and have interesting physical applications and implications.