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This paper presents a significant theoretical breakthrough in quantum information theory by providing an explicit, non-random counterexample to the additivity of minimum output von Neumann entropy. The construction, which mimics free Haar unitary behavior, simultaneously demonstrates violations for Rényi-$p$ entropy across the full range of $1 \le p \le \infty$. These findings refine our understanding of quantum channel capacities and the fundamental limits of information transmission in finite-dimensional systems.
A constructive violation of additivity of minimum output von Neumann entropy
arXiv:2609.23946v1 Announce Type: new 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 also gives a violation of additivity for the minimum output R\'enyi-$p$ entropy for any $1\le p\le\infty$.
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 also gives a violation of additivity for the minimum output Rényi-$p$ entropy for any $1\le p\le\infty$.
arXiv:2609.23946 [quant-ph]
(or arXiv:2609.23946v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.23946 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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