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

• URL: http://arxiv.org/abs/2607.15210v1
• Date: Thu, 16 Jul 2026 17:08:47 GMT
• Title: Counterexamples to additivity of minimum output $p$-Rényi entropy of quantum channels for $p>3/4$ and $0\leq p<1/4$
• Abstract summary: Additivity of minimum output entropies is a central problem in quantum information theory.<n>We prove that for every Rényi order $p$ satisfying either $p>3/4$ or $0leq p1/4$, there exist finite-dimensional projection-induced quantum channels.
• Score: 1.9116784879310027
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every Rényi order $p>1$, at the von Neumann point $p=1$, and near $p=0$, while most of the interval $0<p<1$ has remained open. We prove that for every Rényi order $p$ satisfying either $p>3/4$ or $0\leq p<1/4$, there exist finite-dimensional projection-induced quantum channels such that additivity of the minimum output $p$-Rényi 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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