Abstract
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.
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