Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy distance, with the decoupling error bounded by two sandwiched Rényi conditional entropies. In the asymptotic i.i.d. setting of standard information decoupling via partial trace, we show that this bound is ensemble-tight in quantum relative entropy distance and thereby yields a characterization of the associated decoupling error exponent in the low-cost-rate regime. Leveraging this framework, we derive several operational applications formulated in terms of purified distance: (i) a single-letter expression for the exact error exponent of quantum state merging in terms of Petz-Rényi conditional entropies, and (ii) regularized expressions for the achievable error exponent of entanglement distillation and quantum channel coding in terms of Petz-Rényi coherent informations. We further prove that these achievable bounds are tight for maximally correlated states and generalized dephasing channels, respectively, for the high distillation-rate/coding-rate regimes.

翻译：量子信息解耦是量子信息论中的一项基本原语，支撑着量子物理学中的多种应用。我们证明了一种新颖的单阶解耦定理，该定理以量子相对熵距离表述，其解耦误差由两个夹层Rényi条件熵界定。在通过偏迹进行标准信息解耦的渐近独立同分布设定下，我们证明该界在量子相对熵距离下是系综紧致的，从而在低代价率区域给出了相关解耦误差指数的刻画。利用此框架，我们推导了若干以纯化距离表述的操作性应用：(i) 量子态合并的精确误差指数以Petz-Rényi条件熵表示的单字母表达式，以及(ii) 以Petz-Rényi相干信息表示的纠缠蒸馏与量子信道编码可达误差指数的正则化表达式。我们进一步证明，对于高蒸馏率/编码率区域，这些可达界分别对于最大关联态和广义退相位信道是紧致的。