Broadcasting of imaginarity

Recently, the resource theory of imaginarity was proposed, viewing the imaginary part of a quantum state as a basic resource leading to quantum advantages. As with other quantum resources such as correlations, coherence, and asymmetry, a natural question arises: Can imaginarity resource be broadcast by a real operation which is free in the resource theory of imaginarity? In this work, we introduce two concepts of imaginarity broadcasting. The first pertains to nonreal states, while the second is related to the imaginarity resource. For nonreal states, we demonstrate that a specific type of nonreal states can be broadcast. However, when it comes to broadcasting the imaginarity resource, we get a surprising result that any imaginarity resource can be perfectly broadcast via a real operation. By comparing different (no-)broadcasting theorems, we distinguish the resource theory of imaginarity from the resource theories of correlations, coherence, and asymmetry, and reveal certain distinctive features of the resource theory of imaginarity.