  Coherence distillation is a basic information-theoretic task in the resource
theory of coherence. In this paper, we present the necessary and sufficient
conditions under which a mixed state can be distilled into a pure coherent
state via stochastic incoherent operations (sIOs). With the help of this
result, we further show the following: (i) Any $2$-dimensional coherent state
is distillable via sIOs if and only if it is a pure coherent state; (ii) a
state $\rho$ is n-distillable via sIOs if and only if it is 1-distillable; and
(iii) the set of distillable states via stochastic maximally incoherent
operations is identical to the set of distillable states via sIOs. Finally, we
analyze the reason why sIO is stronger than stochastic strictly incoherent
operations when we use them to distill a coherent state.
