Reduced relative quantum entropy

TL;DR

This paper introduces the concept of reduced relative quantum entropy, proves its convexity, and uses this property to simplify the proof of a theorem by Lieb and Seiringer.

Contribution

The paper defines reduced relative quantum entropy and demonstrates its convexity, providing a new, simplified proof of an existing theorem.

Findings

Reduced relative quantum entropy is convex.

Simplified proof of Lieb and Seiringer's theorem.

New theoretical framework for quantum entropy.

Abstract

We introduce the notion of reduced relative quantum entropy and prove that it is convex. This result is then used to give a simplified proof of a theorem of Lieb and Seiringer.