Based on two types of channel divergences, we introduce four kinds of dynamical imaginarity measures, defined respectively by the deviation of a quantum channel from the set of real channels and from its conjugate channel. We show that they satisfy the desirable properties for a valid dynamical imaginarity measure and reduce to corresponding state imaginarity measures for replacement channels. We also compare them with two existing dynamical measures: Choi state-based dynamical imaginarity and the imaginarity-generating power of quantum channels. Furthermore, when specifying these general divergences to the relative entropy, Jensen-Shannon divergence, and trace distance, we establish explicit connections among them and provide an operational interpretation in the context of quantum channel discrimination. Finally, we evaluate the dynamical imaginarity measures induced by conjugate channels for several typical quantum channels.

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• Quantum information theory