Two imaginarity monotones induced by unified $(\alpha,\beta)$-relative entropy

Complex numbers play a pivotal role in both mathematics and physics, particularly in quantum mechanics, and are extensively utilized to depict the behavior of microscopic particles. Recognizing the significance of complex numbers, a framework of imaginarity resource theory has recently been established. In this work, we propose two types of imaginarity monotones induced by the unified $(\alpha,\beta)$-relative entropy and investigate their properties. Moreover, we give explicit examples to illustrate our results.