  The remarkable phenomenon of catalyst tells us that adding a catalyst could
help state transformation. In this paper, we consider the problem of
catalyst-assisted probabilistic coherence distillation for mixed states under
strictly incoherent operations. To this end, we first present the necessary and
sufficient conditions for distilling a target pure coherent state from an
initial mixed state via stochastic strictly incoherent operations and the
maximal probability of obtaining the target pure state from the initial state.
With the help of these results, we present the necessary and sufficient
conditions for the existence of a catalyst that increases the maximal
transformation probability.
