Measures of imaginarity and quantum state order

Abstract: Complex numbers are widely used in both classical and quantum physics, and play an important role in describing quantum systems and their dynamical behavior. In this paper we study several measures of imaginarity of quantum states in the framework of resource theory, such as the measures based on $l_{1}$ norm, and convex function, etc. We also investigate the influence of the quantum channels on quantum state order for a single-qubit.