Breaking Gaussian incompatibility on continuous variable quantum systems

TL;DR

This paper characterizes Gaussian quantum channels that eliminate measurement incompatibility in continuous variable systems, which is crucial for understanding noise effects on quantum correlations like EPR-steering.

Contribution

It provides a detailed characterization of Gaussian incompatibility breaking channels, extending the concept of entanglement breaking channels to measurement incompatibility in continuous variables.

Findings

Identifies conditions for Gaussian channels to be incompatibility breaking

Links incompatibility breaking channels to noise in quantum information protocols

Enhances understanding of resource theory in noisy continuous variable systems

Abstract

We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.