# Operational characterization of incompatibility of quantum channels with quantum state discrimination

## TL;DR

This paper demonstrates that incompatible quantum channels provide a quantifiable advantage in state discrimination tasks, with the robustness of incompatibility serving as a key measure, and extends this to measurement-channel incompatibility.

## Contribution

It introduces an operational interpretation of channel incompatibility via state discrimination advantage and unifies various types of incompatibility under this framework.

## Key findings

- Incompatible channels outperform compatible ones in state discrimination tasks.
- Robustness of incompatibility quantifies the maximum advantage.
- The results encompass all forms of incompatibility as special cases.

## Abstract

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.