PreprintCC BY 4.0arXiv
Continuity of Regularized Channel Rényi 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.
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BibTeX
@misc{wang2026continuity,
title = {{Continuity of Regularized Channel Rényi Divergences}},
author = {Jinzhao Wang and Yuxiang Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.28635},
eprint = {2609.28635},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28635},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continuity of Regularized Channel Rényi Divergences
AU - Jinzhao Wang
AU - Yuxiang Yang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.28635
UR - https://arxiv.org/abs/2609.28635
AB - 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.
ER -