Decomposition Rules for Quantum Renyi Mutual Information with an Application to Information Exclusion Relations

We prove decomposition rules for quantum Renyi mutual information, generalising the relation $I(A:B) = H(A) - H(A|B)$ to inequalities between Renyi mutual information and Renyi entropy of different orders. The proof uses Beigis generalisation of Reisz-Thorin interpolation to operator norms, and a variation of the argument employed by Dupuis which was used to show chain rules for conditional Renyi entropies. The resulting decomposition rule is then applied to establish an information exclusion relation for Renyi mutual information, generalising the original relation by Hall.