Counterexamples to additivity of minimum output $p$-R\'enyi entropy of quantum channels for all $p\ge 0$

Abstract:The 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 for sufficiently small positive $p$, while much of the interval $0<p<1$ has remained open. In this work, we prove that for every $p>0$ there exist finite-dimensional quantum channels whose minimum output $p$-Rényi entropies violate additivity. Our proof combines two constructions: random projection-induced channels yield nonadditivity for $p>3/4$, and antisymmetric postprocessing extends the violation to all positive Rényi orders. Our estimates also improve the output-dimension bound obtained by Belinschi, Collins, and Nechita for additivity violation of minimum output von Neumann entropy.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Probability (math.PR)

arXiv:2607.15210 [quant-ph]

(or arXiv:2607.15210v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.15210 Focus to learn more arXiv-issued DOI via DataCite

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