Amending coherence-breaking channels via unitary operations

The coherence-breaking channels play a significant role in quantum information theory. We study the coherence-breaking channels and give a method to amend the coherence-breaking channels by applying unitary operations. For given incoherent channel $\Phi$, we give necessary and sufficient conditions for the channel to be a coherence-breaking channel and amend it via unitary operations. For qubit incoherent channels $\Phi$ that are not coherence-breaking ones, we consider the mapping $\Phi\circ\Phi$ and present the conditions for coherence-breaking and channel amendment as well.