Constraints on Gaussian error channels for entanglement swapping with Gaussian measurements

We describe a formalism for Gaussian measurements of continuous-variable quantum systems and use it to derive constraints on entanglement swapping. First, we consider a two-mode entangled Gaussian measurement preceded by independent attenuation channels on the two modes and show that if the sum of the attenuations exceeds 1 then any Gaussian measurement becomes separable and therefore unsuitable for entanglement swapping. We then use a well-known classification of single-mode Gaussian channels to extend this constraint to all pairs of single-mode Gaussian error channels. Finally, we show that our constraints are tight, meaning that Gaussian entanglement swapping is possible if and only if the pair of error channels meets the required constraints.