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
该论文证明了广义量子Stein引理，给出并行区分任意有限维信道与备选信道族的最优第二类错误指数，并构造了显式有限块界，应用于多种信道类型。
AI 中文摘要
我们证明了广义量子Stein引理，用于并行区分任意有限维信道与备选信道族。备选信道族是紧致且凸的，在张量积下封闭，并包含一个忠实的替换信道。在任意固定的第一类错误容限下，最优第二类错误指数等于在备选信道族上最小化的正则化Umegaki信道相对熵，且两个定义极限均存在。输入可在信道使用之间及与参考系统纠缠。主要技术结果构造了精确的迹保持近似，其菱形误差指数级小，且在高于共同指数的每个速率下，由自由信道在完全正序下支配。证明结合了均匀辅助映射近似、支配速率的迭代约简和张量放大。它产生了在每次次指数消失错误下具有迹保持平滑的渐近等分性质、指数级强逆，以及在消失菱形范数扰动下的稳定性。在额外的置换不变性和对插入固定忠实输入态及丢弃其输出的封闭性假设下，我们还证明了显式的有限块完成界。该定量构造使用了加权丢弃、局部算子修正以及与辅助扩展的比较。应用包括态保持、相干受限、协变、纠缠破坏和正部分转置信道。对于等距目标对抗纠缠破坏或正部分转置备选信道，我们获得了精确的有限块测试和平滑公式。
英文摘要
We prove a generalized quantum Stein lemma for parallel discrimination of an arbitrary finite-dimensional channel against families of alternative channels. The alternatives are compact and convex, closed under tensor products, and contain a faithful replacer. At every fixed type-I error tolerance, the optimal type-II error exponent equals the regularized Umegaki channel relative entropy minimized over the alternatives, and both defining limits exist. Inputs may be entangled across channel uses and with a reference system. The main technical result constructs exactly trace-preserving approximations with exponentially small diamond error, dominated in completely positive order by free channels at every rate above the common exponent. The proof combines uniform auxiliary map approximation, iterative reduction of the domination rate, and tensor amplification. It yields asymptotic equipartition with trace-preserving smoothing at every subexponentially vanishing error, an exponential strong converse, and stability under vanishing diamond-norm perturbations. Under additional permutation invariance and closure under insertion of a fixed faithful input state and discarding of its output, we also prove an explicit finite-block completion bound. This quantitative construction uses weighted discarding, local operator corrections, and comparison with auxiliary extensions. Applications include state-preserving, coherence-restricted, covariant, entanglement-breaking, and positive-partial-transpose channels. For isometric targets against entanglement-breaking or positive-partial-transpose alternatives, we obtain exact finite-block testing and smoothing formulas.
Comments43 pages
