Bounds for imaginarity of quantum superpositions

Abstract

Abstract Complex numbers play a key role in classical and quantum physics. Recently, the comprehensive formulation of the resource theory of imaginarity was proposed and various computable and meaningful measures of imaginarity were identified. In this work, we investigate the bounds for imaginarity of quantum superpositions in high dimension using the geometric imaginarity. We establish the relationship between the imaginarity of the superposition of quantum states and the imaginarity of the states being superposed.