发表机构
Institute of Software, Chinese Academy of Sciences; University of Chinese Academy of Sciences; Department of Computer Science and Technology, Tsinghua University（中国科学院软件研究所; 中国科学院大学; 清华大学计算机科学与技术系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文建立了量子信道Stein引理，证明在任意自适应策略下指数级强逆定理，并给出最优第二类指数等于正则化信道相对熵的结论。
AI 中文摘要
我们在每个固定的第一类错误容忍度$(0,1)$下建立了量子信道Stein引理，并证明了在任意自适应策略下指数级强逆定理。对于任何有限维信道对，最优第二类指数等于正则化信道相对熵，并且由并行策略达到。当该散度有限时，任何严格更大的第二类速率都会迫使接受原假设的概率指数衰减，且该衰减在策略和量子记忆上一致。证明依赖于一个均匀的Stinespring近似：通过向环境应用辅助线性映射，零扩张的张量幂被替代扩张的张量幂近似。在正则化相对熵之上的任何速率下，算子范数误差在平方范数约束下指数小。我们通过迭代速率降低和具有精确残差的固定块张量展开，从一个弱测试界构造该近似。它蕴含正则化夹心Rényi信道散度在一阶处的右连续性，这通过信道链式法则产生自适应逆定理。我们还获得了尖锐的曲棍球棒阈值和固定及次指数消失的钻石范数误差下的子信道平滑渐近等分性质。
英文摘要
We establish the quantum channel Stein lemma at every fixed type-I error tolerance in $(0,1)$ and prove an exponential strong converse under arbitrary adaptive strategies. For any finite-dimensional channel pair, the optimal type-II exponent equals the regularized channel relative entropy and is attained by parallel strategies. When this divergence is finite, every strictly larger type-II rate forces the probability of accepting the null hypothesis to decay exponentially, uniformly over strategies and quantum memories. The proof rests on a uniform Stinespring approximation: tensor powers of the null dilation are approximated by tensor powers of the alternative dilation after applying an auxiliary linear map to the environment. The operator-norm error is exponentially small under a squared-norm bound at any rate above the regularized relative entropy. We construct the approximation from a weak testing bound by iterative rate reduction and a fixed-block tensor expansion with an exact residual. It implies right continuity at order one of the regularized sandwiched Rényi channel divergence, which yields the adaptive converse through the channel chain rule. We also obtain a sharp hockey-stick threshold and a subchannel smoothing asymptotic equipartition property for fixed and subexponentially vanishing diamond-norm errors.
Comments24 pages
