  Quantum states transformation under free operations plays a central role in
the resource theory of coherence. In this paper, we investigate the
transformation from a mixed coherent state into a pure one by using both
incoherent operations and stochastic incoherent operations. We show that
contrary to the strictly incoherent operations and the stochastic strictly
incoherent operations, both the incoherent operations and the stochastic
incoherent operations can increase the dimension of the maximal pure coherent
subspace of a state. This means that the incoherent operations are generally
stronger than the strictly incoherent operations when we want to transform a
mixed coherent state into a pure coherent one. Our findings can also be
interpreted as confirming the ability of incoherent operations to enhance the
coherence of mixed states relative to certain coherence monotones under
strictly incoherent operations.
