Quantum coherence via skew information for quantum channels

Recently, various resource theories of physical properties are extensively studied. In particular, the resource theory of quantum coherence with respect to a quantum channel is also investigated. In this paper, instead of quantifying coherence existing in a state, we present a quantifier of coherence for a quantum channel via skew information. We then show that the coherence quantifier fits the framework of quantifying coherence of a quantum channel. As an application of our result, we show that the superiority of a quantum channel in sub-superchannel discrimination can be precisely characterized by the coherence via skew information of a quantum channel. A similar notion induced by Hellinger distance can also be established for a quantum channel, which we called the Hellinger distance coherence of a quantum channel. Moreover, we show that there is a quantitative relationship between the coherence via skew information of a quantum channel and the Hellinger distance coherence measure of this quantum channel.