  In quantum information, most information processing processes involve quantum
channels. One manifestation of a quantum channel is quantum operation acting on
quantum states. The coherence of quantum operations can be considered as a
quantum resource, which can be exploited to perform certain quantum tasks. From
the viewpoint of Choi-Jamio{\l}kowski isomorphism, we study the coherence of
quantum operations in the framework of resource theory. We define the phase-out
superoperation and give the operation which transforms the Choi-Jamio{\l}kowski
state of a quantum operation to the Choi-Jamio{\l}kowski state of the another
quantum operation obtained by using the phase-out superoperation to act on the
quantum operation. The set of maximally incoherent superoperations, the set of
nonactivating coherent superoperations and the set of de-phase incoherent
superoperations are defined and we prove that these sets are closed to compound
operation and convex combination of quantum superoperations. Further, we
introduce the fidelity coherence measure of quantum operations and obtain the
exact form of the fidelity coherence measure of the unitary operations on the
single qubit.
