Almost One Bit Violation of Minimum-Output Rényi Entropy Additivity Simultaneously at All Orders

Abstract

We prove that minimum-output Rényi-entropy additivity can fail by almost one bit simultaneously at every nonnegative order. For every ε∈(0,log2), there exists a finite-dimensional quantum channel with a real Stinespring isometry such that the same maximally entangled input witnesses a tensor-square entropy gap of at least log2−ε for all p∈[0,∞]. The output dimension can be chosen to be O(ε⁻³) as ε↓0. The construction uses direct products of free groups: tensorized Haagerup estimates control the one-copy outputs, while commutation between distinct factors forces exact Bell-branch collisions at two copies. Strong convergence gives both an existential realization through finite-dimensional representations of right-angled Artin groups followed by realification, and a Haar-orthogonal model whose success probability tends to one as the matrix dimension grows. We also determine the exact Bell quotient, prove asymptotically sharp regular-radius bounds, and show that the cubic output-dimension scale is optimal within the present purity--rank certificate.

A constructive violation of additivity of minimum output von Neumann entropy
Laura Shou, Alexey V. Gorshkov
arXiv24 Sep 2026PreprintarXiv licenceFull textMathematical physics Quantum physics & quantum informationarXiv
Counterexamples to additivity of minimum output p-Rényi entropy of quantum channels for all p≥ 0
Debbie Leung, Benjamin Lovitz, Ion Nechita +1
arXiv5 Oct 2026PreprintCC BY 4.0Full textMathematical physics ProbabilityarXiv
Almost-Uniform Bayesian Convergence to the Truth Is Not Characterized by Countable Additivity on Conditional Hitting Times
M. Ali Khan, Arthur Paul Pedersen, Maxwell B. Stinchcombe
arXiv17 Sep 2026PreprintCC BY 4.0Full textAnalysis & PDEs Geometry & topologyarXiv
Simultaneously small continued fraction entropy and base b entropy
Faruk Temur
arXiv14 Sep 2026PreprintarXiv licenceFull textAlgebra & number theoryarXiv
The Minimum Number of Measurements for Almost-Everywhere Complex Phase Retrieval
Zhiqiang Xu
arXiv28 Aug 2026PreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv

Cite

BibTeX RIS

BibTeX

@misc{zhen2026almost,
  title = {{Almost One Bit Violation of Minimum-Output Rényi Entropy Additivity Simultaneously at All Orders}},
  author = {Guocheng Zhen and Chengkai Zhu and Ranyiliu Chen and Xin Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18747},
  eprint = {2609.18747},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18747},
}

RIS

TY  - UNPB
TI  - Almost One Bit Violation of Minimum-Output Rényi Entropy Additivity Simultaneously at All Orders
AU  - Guocheng Zhen
AU  - Chengkai Zhu
AU  - Ranyiliu Chen
AU  - Xin Wang
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18747
UR  - https://arxiv.org/abs/2609.18747
AB  - We prove that minimum-output Rényi-entropy additivity can fail by almost one bit simultaneously at every nonnegative order. For every ε∈(0,log2), there exists a finite-dimensional quantum channel with a real Stinespring isometry such that the same maximally entangled input witnesses a tensor-square entropy gap of at least log2−ε for all p∈[0,∞]. The output dimension can be chosen to be O(ε^−3) as ε↓0. The construction uses direct products of free groups: tensorized Haagerup estimates control the one-copy outputs, while commutation between distinct factors forces exact Bell-branch collisions at two copies. Strong convergence gives both an existential realization through finite-dimensional representations of right-angled Artin groups followed by realification, and a Haar-orthogonal model whose success probability tends to one as the matrix dimension grows. We also determine the exact Bell quotient, prove asymptotically sharp regular-radius bounds, and show that the cubic output-dimension scale is optimal within the present purity--rank certificate.
ER  -

Abstract

Related

Cite