Counterexamples to additivity of minimum output p-Rényi entropy of quantum channels for all p≥ 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.
Related
- A constructive violation of additivity of minimum output von Neumann entropy
- Almost One Bit Violation of Minimum-Output Rényi Entropy Additivity Simultaneously at All Orders
- Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions
- Minimum orders of clique oddomorphism counterexamples
- On minimum-size matroid counterexamples to the multiplicative Merino--Welsh inequality
BibTeX
@misc{leung2026counterexamples,
title = {{Counterexamples to additivity of minimum output $p$-Rényi entropy of quantum channels for all $p\ge 0$}},
author = {Debbie Leung and Benjamin Lovitz and Ion Nechita and Peixue Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.15210},
eprint = {2607.15210},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15210},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Counterexamples to additivity of minimum output p-Rényi entropy of quantum channels for all p≥ 0
AU - Debbie Leung
AU - Benjamin Lovitz
AU - Ion Nechita
AU - Peixue Wu
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2607.15210
UR - https://arxiv.org/abs/2607.15210
AB - 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.
ER -