We introduce a task that we call partial decoupling, in which a bipartite quantum state is transformed by a unitary operation on one of the two subsystems and then is subject to the action of a quantum channel. We assume that the subsystem is decomposed into a direct-sum-product form, which often appears in the context of quantum information theory. The unitary is chosen at random from the set of unitaries having a simple form under the decomposition. The goal of the task is to make the final state, for typical choices of the unitary, close to the averaged final state over the unitaries. We consider a one-shot scenario, and derive upper and lower bounds on the average distance between the two states. The bounds are represented simply in terms of smooth conditional entropies of quantum states involving the initial state, the channel and the decomposition. Thereby we provide generalizations of the one-shot decoupling theorem. The obtained result would lead to further development of the decoupling approaches in quantum information theory and fundamental physics.

我们引入了一个我们称之为部分解耦的任务，其中二分量子态通过对两个子系统之一的幺正操作进行转换，然后受到量子通道的作用。我们假设子系统被分解为直和积形式，这种形式经常出现在量子信息论的上下文中。幺正是从分解下具有简单形式的幺正集合中随机选择的。任务的目标是使最终状态（对于酉的典型选择）接近酉的平均最终状态。我们考虑一次性场景，并推导出两个状态之间平均距离的上限和下限。边界简单地用涉及初始状态、通道和分解的量子状态的平滑条件熵来表示。因此，我们提供了一次性解耦定理的推广。所获得的结果将导致量子信息理论和基础物理学中解耦方法的进一步发展。