On Uhlmann's proof of the Monotonicity of the Relative Entropy

TL;DR

This paper provides a clear, self-contained presentation of Uhlmann's theorem on the monotonicity of relative entropy under quantum operations, including its general form and illustrative examples.

Contribution

It offers a comprehensive, accessible exposition of Uhlmann's proof and extends the theorem to a more general setting with practical examples.

Findings

Confirmed the monotonicity of relative entropy under CPTP maps

Extended the theorem to a more general framework

Provided meaningful examples illustrating the theorem

Abstract

This article presents in a self-contained way A. Uhlmann's celebrated Theorem of monotonicity of the relative entropy under completely positive and trace preserving maps. The Theorem is presented in its more general form and meaningful examples are given.