Incompatibility breaking quantum channels

TL;DR

This paper introduces and analyzes incompatibility breaking quantum channels, which are noise processes that completely eliminate measurement incompatibility, a key quantum feature in protocols like EPR-steering.

Contribution

It defines the concept of incompatibility breaking channels and explores their properties, extending the understanding of noise effects on quantum measurement incompatibility.

Findings

Compatible measurements cannot become incompatible via channels

Certain channels can fully destroy measurement incompatibility

Implications for noise robustness in quantum steering

Abstract

A typical bipartite quantum protocol, such as EPR-steering, relies on two quantum features, entanglement of states and incompatibility of measurements. Noise can delete both of these quantum features. In this work we study the behavior of incompatibility under noisy quantum channels. The starting point for our investigation is the observation that compatible measurements cannot become incompatible by the action of any channel. We focus our attention to channels which completely destroy the incompatibility of various relevant sets of measurements. We call such channels incompatibility breaking, in analogy to the concept of entanglement breaking channels. This notion is relevant especially for the understanding of noise-robustness of the local measurement resources for steering.