Freezing imaginarity measures with real operations

Abstract Imaginarity plays an essential role in many quantum information processing tasks. Usually, real operations do not increase imaginarity measures. In present work, we aim to discuss freezing of imaginarity measures with real operations. It is proved that a real operation Φ freezes all imaginarity measures of a state ρ if and only if it freezes the relative entropy measure of imaginarity of the state ρ . In the qubit case, real operations that freeze imaginarity measures based on trace distance and relative entropy are characterized, respectively. Moreover, the freezing of imaginarity measure based on trace distance is not necessarily dilated into multipartite systems, while that based on the Tsallis relative entropy can be dilated into multipartite systems. Finally, we characterize real local operations that freeze the imaginarity measure based on trace distance of a special type of X-states in a multi-qubit system.