Quantifying imaginarity of quantum operations

Complex numbers are theoretically proved and experimentally confirmed as necessary in quantum mechanics and quantum information, and a resource theory of imaginarity of quantum states has been established. In this work, we establish a framework to quantify the imaginarity of quantum operations from the perspective of the ability to create or detect imaginarity, following the idea by Theurer et al. (Phys. Rev. Lett. 122, 190405 (2019)) used in coherence theory. We introduce two types of imaginarity measures of quantum operations based on the norm and the weight, investigate their properties and relations, derive the analytical formulas of the measure under the trace norm for qubit unitary operations, and present some applications in the tasks of channel discrimination and the entanglement-assisted exclusion. The results provide new insights into the imaginarity of operations and deepen our understanding of dynamical imaginarity.