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 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 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.

中文翻译：

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量子人一互信息分解规则在信息排除关系中的应用

我们证明了量子人一互信息的分解规则，将关系$I(A:B) = H(A) - H(A|B)$推广到人一互信息和不同阶人一熵之间的不等式。证明使用 Beigi 对 Reisz-Thorin 插值的推广到算子范数，以及 Dupuis 使用的参数的变体，用于显示条件 Renyi 熵的链式规则。然后应用得到的分解规则来建立 Renyi 互信息的信息排除关系，通过 Hall 推广原始关系。