发表机构
Zyphra; QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong（Zyphra; 量子信息与计算倡议，计算与数据科学学院，香港大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明有限维量子信道的正则化夹心Rényi散度在阶数趋于1时收敛于正则化相对熵，并利用信道曲棍球棒散度导出指数强逆、零一检验定律和子信道渐近等分性质。
AI 中文摘要
我们证明了有限维量子信道的正则化、稳定化夹心Rényi散度在Rényi阶趋于1时收敛于其正则化相对熵。关键工具是信道曲棍球棒散度：Gour的Stinespring近似界和Schatten范数估计将低于1的渐近界放大为在更高阈值速率下的指数衰减。对于具有有限最大相对熵的信道对，已知的操作性联系随后给出并行和自适应区分的指数强逆、一个尖锐的零一检验定律以及子信道渐近等分性质。
英文摘要
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.
Comments12 pages; comments are welcome; v2: updated references for concurrent works, add a Lean certificate for our proof: https://github.com/JWang226/continuity-of-regularized-channel-renyi-divergence
