Almost One Bit Violation of Minimum-Output R\'enyi 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 $\varepsilon\in(0,\log2)$, 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 $\log2-\varepsilon$ for all $p\in[0,\infty]$. The output dimension can be chosen to be $O(\varepsilon^{-3})$ as $\varepsilon\downarrow0$. 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.

Quantum Physics (quant-ph); Operator Algebras (math.OA)

arXiv:2609.18747 [quant-ph]

(or arXiv:2609.18747v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.18747 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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