Incompatibility breaking quantum channels

Abstract

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