Monotonicity of a relative R\'enyi entropy

TL;DR

This paper proves that a recent definition of relative Re9nyi entropy is monotone under quantum operations, confirming a conjecture and advancing understanding of quantum information measures.

Contribution

It establishes the monotonicity of a recent relative Re9nyi entropy definition under CPTP maps, confirming a key conjecture.

Findings

Proves monotonicity of the new relative Re9nyi entropy

Confirms a conjecture by Mfcller-Lennert et al.

Advances theoretical understanding of quantum entropy measures.

Abstract

We show that a recent definition of relative R\'enyi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of M\"uller-Lennert et al.