No-broadcasting of magic states

From both intuitive and physical perspectives, it is generally recognized that within a resource theory framework, free operations cannot broadcast a resource state due to their inability to generate resource from free states. In the stabilizer formalism of fault-tolerant quantum computation, the basic ingredients of the corresponding resource theory consist of stabilizer states as free states and stabilizer operations as free operations. The celebrated Gottesman-Knill theorem shows that quantum advantages over classical computation come from the magic (nonstabilizer) resource, such as magic states or non-Clifford gates. In this work, we prove that broadcasting of any magic state via stabilizer operations is impossible, which is reminiscent of the no-broadcasting theorems for noncommuting states or quantum correlations. We further derive a trade-off relation between the magic resource consumed in the initial system and that gained in the target system. These results characterize magic states in the stabilizer formalism from the broadcasting angle, and may have implications for distributed quantum computation and quantum secret sharing.