  As an important quantum resource, quantum coherence play key role in quantum
information processing. It is often concerned with manipulation of families of
quantum states rather than individual states in isolation. Given two pairs of
coherent states $(\rho_1,\rho_2)$ and $(\sigma_1,\sigma_2)$, we are aimed to
study how can we determine if there exists a strictly incoherent operation
$\Phi$ such that $\Phi(\rho_i) =\sigma_i,i = 1,2$. This is also a classic
question in quantum hypothesis testing. In this note, structural
characterization of coherent preorder under strongly incoherent operations is
provided. Basing on the characterization, we propose an approach to realize
coherence distillation from rank-two mixed coherent states to $q$-level
maximally coherent states. In addition, one scheme of coherence manipulation
between rank-two mixed states is also presented.
