  A collection of quantum channels is called incompatible if they cannot be
obtained as marginals from a single channel. No-cloning theorem is the most
prominent instance of incompatibility of quantum channels. We show that every
collection of incompatible channels can be more useful than compatible ones as
preprocessings in a state discrimination task with multiple ensembles of
states. This is done by showing that the robustness of channel incompatibility
which is a measure for incompatibility of channels exactly quantifies the
maximum advantage in the state discrimination. We also show that
incompatibility of quantum measurement and channel has a similar operational
interpretation. Finally, we demonstrate that our result with respect to channel
incompatibility includes all other kinds of incompatibility as special cases.
