We consider the distillation of quantum coherence in the one-shot setting. The protocol is based on the probabilistic coherence distillation assisted by another party. In this context, coherent states including pure states and mixed states can be transformed into maximally coherent pure state with some probability and the maximal probability is defined as the maximal success probability of assistance. Then we show an upper bound for the maximal success probability of assistance for transforming d-dimensional mixed state to d-dimensional maximally coherent pure state. This upper bound is reached by all mixed states in two- and three-dimensional system and all incoherent states. A lower bound of the maximal success probability of assistance for the full-rank quantum states is also proposed. We also show an upper bound for the maximal success probability of assistance for transforming d-dimensional mixed state to \(m\ (m\le d)\)-dimensional maximally coherent pure state in general case.

我们考虑在单次设置中量子相干性的提炼。该协议基于另一方协助进行的概率相干提纯。在这种情况下，包括纯态和混合态在内的相干态可以一定的概率被转换成最大相干的纯态，并且最大概率被定义为协助的最大成功概率。然后，我们展示的上界的援助的最大成功概率转化d维混合状态d维最大相干纯态。二维系统和三维系统中的所有混合状态以及所有非相干状态都可以达到此上限。还提出了对满秩量子态的最大辅助成功概率的下限。在一般情况下，我们还显示了将d维混合状态转换为\（m \（m \ le d）\）维最大相干纯状态的辅助方法的最大成功概率的上限。