In this paper, we consider the standard quantum information decoupling, in which Alice aims to decouple her system from the environment by local operations and discarding some of her systems. To achieve an $\varepsilon$-decoupling with trace distance as the error criterion, we establish a near-optimal one-shot characterization for the largest dimension of the remainder system in terms of the conditional $(1-\varepsilon)$-hypothesis-testing entropy. When the underlying system is independent and identically prepared, our result leads to the matched second-order rate as well as the matched moderate deviation rate. As an application, we find an achievability bound in entanglement distillation protocol, where the objective is for Alice and Bob to transform their quantum state to maximally entangled state with largest possible dimension using only local operations and one-way classical communications.

翻译：本文研究标准量子信息解耦问题，其中Alice旨在通过局域操作并丢弃部分系统，将其系统与环境解耦。以迹距离作为误差准则实现$\varepsilon$-解耦时，我们基于条件$(1-\varepsilon)$-假设检验熵建立了剩余系统最大维度的近最优单次刻画。当底层系统独立同分布时，该结果导出了匹配的二阶率及匹配的适中偏差率。作为应用，我们在纠缠蒸馏协议中找到了可达性界——该协议的目标是Alice和Bob仅通过局域操作和单向经典通信，将其量子态转化为最大可能维度的最大纠缠态。