An intuitive proof of the data processing inequality

TL;DR

This paper presents a simplified, intuitive proof of the data processing inequality for quantum information, specifically deriving the von Neumann entropy case from the smooth min-entropy using a new proof of the quantum asymptotic equipartition property.

Contribution

It offers a new, simplified proof of the quantum asymptotic equipartition property, leading to a self-contained proof of the data processing inequality for von Neumann entropy.

Findings

Simplified proof of the quantum asymptotic equipartition property

Self-contained proof of the data processing inequality for von Neumann entropy

Clarifies the relationship between smooth min-entropy and von Neumann entropy

Abstract

The data processing inequality (DPI) is a fundamental feature of information theory. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. When the smooth min-entropy is used as the relevant information measure, then the DPI follows immediately from the definition of the entropy. The DPI for the von Neumann entropy is then obtained by specializing the DPI for the smooth min-entropy by using the quantum asymptotic equipartition property (QAEP). We provide a new, simplified proof of the QAEP and therefore obtain a self-contained proof of the DPI for the von Neumann entropy.