Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum channels is directly related to the maximally coherent channels under a particular class of superoperations, which results in an operational interpretation of the maximum relative entropy for coherence of quantum channels. We also introduce the conception of sub-superchannels and sub-superchannel discrimination. For any quantum channels, we show that the advantage of quantum channels in sub-superchannel discrimination can be exactly characterized by the maximum relative entropy of coherence for quantum channels. Similar to the maximum relative entropy of coherence for channels, the robustness of coherence for quantum channels has also been investigated. We show that the maximum relative entropy of coherence for channels provides new operational interpretations of robustness of coherence for quantum channels and illustrates the equivalence of the dephasing-covariant superchannels, incoherent superchannels, and strictly incoherent superchannels in these two operational tasks.

基于量化量子信道相干性的资源理论，我们通过最大相对熵引入了一种新的量子信道相干性量词。我们证明了量子通道相干的最大相对熵与特定类别超运算下的最大相干通道直接相关，这导致对量子通道相干的最大相对熵的操作解释。我们还介绍了子超级信道和子超级信道鉴别的概念。对于任何量子信道，我们证明了量子信道在子超信道区分中的优势可以准确地用量子信道相干的最大相对熵来表征。类似于通道相干的最大相对熵，还研究了量子通道相干性的鲁棒性。我们表明，通道相干的最大相对熵为量子通道的相干稳健性提供了新的操作解释，并说明了移相协变超通道、非相干超通道和严格非相干超通道在这两个操作任务中的等效性。