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

Abstract

We prove decomposition rules for quantum Rényi mutual information, generalising the relation $I(A:B)=H(A)-H(A|B)$ to inequalities between Rényi mutual information and Rényi 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 Rényi entropies. The resulting decomposition rule is then applied to establish an information exclusion relation for Rényi mutual information, generalising the original relation by Hall.

v2 - Modified section headings, fixed typos in references. v3 - Fixed other typos, minor addition to introduction, reflects published version