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

Debbie Leung, Benjamin Lovitz, Ion Nechita +1 more

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.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.

quant-pharXiv:2607.15210Jul 17, 20260 citations

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Counterexamples to additivity of minimum output

p

-Rényi entropy of quantum channels for all

p\ge 0

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.