Superdense coding in the resource theory of asymmetry

We analyze the task of encoding classical information into a quantum system under restriction by symmetry. Motivated an analogy between resource theories asymmetry and entanglement, we ask whether analog superdense coding is possible in former. I.e., investigate capacity asymmetric state can be strictly larger than that any symmetric whereas latter positive constant. prove this if only unitary representation symmetry non-Abelian reducible. The result provides information-theoretical classification symmetries systems. also discuss possibility other theories.