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Based on the resource theory for quantifying the coherence of quantumchannels, we introduce a new coherence quantifier for quantum channels viamaximum relative entropy. We prove that the maximum relative entropy forcoherence of quantum channels is directly related to the maximally coherentchannels under a particular class of superoperations, which results in anoperational interpretation of the maximum relative entropy for coherence ofquantum channels. We also introduce the conception of sub-superchannels andsub-superchannel discrimination. For any quantum channels, we show that theadvantage of quantum channels in sub-superchannel discrimination can be exactlycharacterized by the maximum relative entropy of coherence for quantumchannels. Similar to the maximum relative entropy of coherence for channels,the robustness of coherence for quantum channels has also been investigated. Weshow that the maximum relative entropy of coherence for channels provides newoperational interpretations of robustness of coherence for quantum channels andillustrates the equivalence of the dephasing-covariant superchannels,incoherent superchannels, and strictly incoherent superchannels in these twooperational tasks.

Maximum Relative Entropy of Coherence for Quantum Channels