Continuity of Regularized Channel R\'enyi Divergences

Abstract:We prove that the regularized, stabilized sandwiched Rényi divergence of finite-dimensional quantum channels converges to their regularized relative entropy as the Rényi order tends to one. The key tool is the channel hockey-stick divergence: Gour's Stinespring approximation bound and a Schatten norm estimate amplify an asymptotic bound below one into exponential decay at higher threshold rates. For channel pairs with finite max-relative entropy, known operational connections then give exponential strong converses for parallel and adaptive discrimination, a sharp zero--one testing law, and the subchannel asymptotic equipartition property.

Quantum Physics (quant-ph); Information Theory (cs.IT); Mathematical Physics (math-ph)

arXiv:2609.28635 [quant-ph]

(or arXiv:2609.28635v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.28635 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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