  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.
