Exclusion principle for quantum dense coding

We show that the classical capacity of a quantum state, as quantified by its ability to perform dense coding, respects an exclusion principle, for arbitrary pure or mixed three-party states in any dimension. This states that no two bipartite states which are reduced states of a common tripartite quantum state can have simultaneous quantum advantage in dense coding. The exclusion principle is robust against noise. Such a principle also holds for an arbitrary number of parties. This exclusion principle is independent of the content and distribution of entanglement in the multipartite state.