Operational characterization of incompatibility of quantum channels with quantum state discrimination
Junki Mori
Abstract
A collection of quantum channels is called incompatible if they cannot be obtained as marginals from a single channel. The 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.