Coherence weight of quantum channels

Quantifying coherence has received significant attention in recent years. Many research is focus on the resource theory of static coherence. In this paper, we introduce the coherence weight of quantum channel to study the quantum resource theory of dynamical coherence. The free channel is classical channel and the free super-channel are the maximally incoherent superchannels (MISC) and incoherent superchannels (ISC). We first study some basic properties (such as convexity and monotonicity) of coherence weight of quantum channel. By introducing entanglement-assisted super-subchannel exclusion task, we show that the advantage of coherent channels in such task. Finally, we compute the coherence weight of quantum channel for some channels.