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In quantum information, most information processing processes involve quantumchannels. One manifestation of a quantum channel is quantum operation acting onquantum states. The coherence of quantum operations can be considered as aquantum resource, which can be exploited to perform certain quantum tasks. Fromthe viewpoint of Choi-Jamio{\l}kowski isomorphism, we study the coherence ofquantum operations in the framework of resource theory. We define the phase-outsuperoperation and give the operation which transforms the Choi-Jamio{\l}kowskistate of a quantum operation to the Choi-Jamio{\l}kowski state of the anotherquantum operation obtained by using the phase-out superoperation to act on thequantum operation. The set of maximally incoherent superoperations, the set ofnonactivating coherent superoperations and the set of de-phase incoherentsuperoperations are defined and we prove that these sets are closed to compoundoperation and convex combination of quantum superoperations. Further, weintroduce the fidelity coherence measure of quantum operations and obtain theexact form of the fidelity coherence measure of the unitary operations on thesingle qubit.

On coherence of quantum operations by using Choi-Jamio{\l}kowski isomorphism