We adequately characterize the distillability of quantum coherence under the maximally incoherent operations (MIO) in the probabilistic distillation’s framework. In particular, we prove that every non-full-rank coherent state exhibits a nonzero probability in the task of probabilistic deterministic distillation. Moreover, we find that the maximal coherence, a computable coherence monotone under strictly incoherent operations (SIO), is a coherence monotone under incoherent operations (IO) and add the proof that the maximal coherence fulfills strong monotonicity under SIO. It is suggested that the maximal success probability of distillation from all coherent states whose density matrix does not contain any rank-one submatrix is less than 1 under IO and equals 0 under SIO. Finally, we present an explicit example for probabilistic distillation under IO and show that a class of non-full rank 3-dimensional states possesses the probabilistic distillability.

我们充分地描述了在概率蒸馏框架下最大非相干运算（MIO）下量子相干的可蒸馏性。特别是，我们证明了在概率确定性蒸馏任务中，每个非满秩相干态都显示出非零概率。此外，我们发现最大相干性（严格不相干运算（SIO）下的可计算相干单调）是非相干运算（IO）下的相干单调，并补充证明最大相干性满足强单调性在SIO下。建议从其密度矩阵不包含任何秩一子矩阵的所有相干状态进行蒸馏的最大成功概率在IO下小于1，在SIO下等于0。最后，我们给出了一个在IO下进行概率蒸馏的显式示例，并表明一类非全等级3维状态具有概率可蒸馏性。