Comment on "Stronger subadditivity of entropy" by Lieb and Seiringer math-ph/0412009

TL;DR

This paper explains how to derive Lieb and Seiringer's entropy subadditivity results using monotonicity of relative entropy, and discusses how their approach can be used to achieve tighter bounds in various scenarios.

Contribution

It provides a new derivation of Lieb and Seiringer's results and demonstrates how to improve bounds using their method.

Findings

Derivation of entropy subadditivity from relative entropy monotonicity

Method to obtain tighter bounds in entropy inequalities

Application of Lieb and Seiringer's approach to various problems

Abstract

We show how recent results of Lieb and Seiringer [math-ph/0412009; Phys. Rev. A 71, 062329 (2005)] can be obtained from repeated use of the monotonicity of relative entropy under partial traces, and explain how to use their approach to obtain tighter bounds in many situations.