Generalized quantum Jensen-Shannon divergence of imaginarity

Abstract

We utilize two types of generalized quantum Jensen-Shannon divergence to detect the imaginarity of quantum states from two perspectives: the deviations of the state from its conjugate state and from its real part. We reveal their basic properties and demonstrate that the generalized quantum Jensen-Shannon divergence of imaginarity via Tsallis relative entropy are valid imaginarity measures, while those via Tsallis entropy are merely imaginarity quantifiers. Furthermore, we establish two complementary relations between the imaginarity and uncertainty of a quantum state via Tsallis entropy. We also connect the four imaginarity quantifiers provided in this work with three existing imaginarity measures: trace norm of imaginarity, relative entropy of imaginarity and Tsallis relative entropy of imaginarity. Finally, we evaluate the imaginarity of pure states and the maximally imaginary mixed states and find that the trends of various imaginarity quantifiers with the state parameter can be affected by the measure parameter, and vice versa.