Counterexamples to additivity of minimum output $p$-Rényi entropy of quantum channels for all $p\ge 0$
Year: 2026
Type: preprint
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 $00$ 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.
Source: arXiv (Cornell University)
Institutions: Concordia University, University of Waterloo
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169625508