  We prove decomposition rules for quantum R\'enyi mutual information,
generalising the relation $I(A:B) = H(A) - H(A|B)$ to inequalities between
R\'enyi mutual information and R\'enyi entropy of different orders. The proof
uses Beigi's 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 R\'enyi entropies. The resulting decomposition rule is
then applied to establish an information exclusion relation for R\'enyi mutual
information, generalising the original relation by Hall.
