A constructive violation of additivity of minimum output von Neumann entropy

Abstract

We give an explicit non-random example of nonadditivity of minimum output von Neumann entropy. The proof uses a finite-dimensional construction which imitates free Haar unitary behavior. The same channel gives a violation of additivity for the minimum output Rényi-$p$ entropy for any $p\in [1,\infty ]$. Additionally, given any $p_0>0$ and $\mathfrak{g}>0$, we extend the construction to obtain an explicit non-random channel which has entropy gap $\ge \mathfrak{g}$ uniformly over $p\in [p_0,\infty ]$.

arXiv comment22 pages; v2 added Theorem 1.3/Appendix B on extension to large entropy gap and p\ge p_0>0