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arXiv · 2607.15210

Counterexamples to additivity of minimum output $p$-R\'enyi entropy of quantum channels for $p>3/4$ and $0\leq p<1/4$

Debbie Leung·Benjamin Lovitz·Peixue Wu
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Abstract

Additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every R\'enyi order $p>1$, at the von Neumann point $p=1$, and near $p=0$, while most of the interval $0 3/4$ or $0\leq p<1/4$, there exist finite-dimensional projection-induced quantum channels such that additivity of the minimum output $p$-R\'enyi entropy fails. The proof combines two correlated random-projection constructions: a product-conjugate Bell-state witness for $p>3/4$, and a transpose-complement rank-defect witness for $p<1/4$. Thus the unresolved part of $0<p<1$ is reduced to $[1/4,3/4]$. Our estimates also improve the output dimension threshold for additivity violation of minimum output von Neumann entropy, first established in Belinschi, Collins and Nechida.

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Debbie Leung, Benjamin Lovitz, Peixue Wu. 2026-07-16. Counterexamples to additivity of minimum output $p$-R\'enyi entropy of quantum channels for $p>3/4$ and $0\leq p<1/4$. https://arxiv.org/abs/2607.15210

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