Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a rule is the data-processing inequality, which tells us that if the same channel is applied to both inputs then the divergence cannot increase. Based on direct matrix analysis methods, we derive several R\'enyi divergence chain rules for channels in the quantum setting. Our results simplify and in some cases generalise previous derivations in the literature.

翻译：频道的不同链规则将一对渠道投入的差异与相应渠道产出的差异联系起来。这种规则的一个重要特殊情况是数据处理不平等,它告诉我们,如果对两种投入都适用同一渠道,那么这种差异就不会增加。根据直接矩阵分析方法,我们在量子设置中为频道得出若干R\'enyi差异链规则。我们的结果简化了文献中以往的推理,有时也概括了文献中的推理。