Non-Additivity of Minimum Output p-$\mathbf{R\acute{e}nyi}$ Entropy

TL;DR

This paper demonstrates that the minimum output p-Rényi entropy is non-additive for certain ranges of p, extending Hastings' approach to a broader class of entropy measures.

Contribution

It shows non-additivity of minimum output p-Rényi entropy for specific p ranges, generalizing previous results on entropy additivity.

Findings

Non-additivity for p in (0, p0) and (1 - p0, 1)

Extension of Hastings' approach to p-Rényi entropy

Identification of p0 approximately equal to 0.2855

Abstract

Hastings disproved additivity conjecture for minimum output entropy by using random unitary channels. In this note, we employ his approach to show that minimum output $p-$R\'{e}nyi entropy is non-additive for $p\in(0,p_0)\cup(1-p_0,1)$ where $p_0\approx 0.2855$.