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

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 $p-$Rényi entropy is non-additive for $p\in (0,p_0)\cup (1-p_0,1)$ where $p_0\approx 0.2855$.

This paper has been withdrawn by the author due to a crucial error