Operational characterization of incompatibility of quantum channels with quantum state discrimination

Understand

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.