Features of preparable entangled states in Gaussian quantum networks

Large-scale quantum networks have been employed to overcome practical constraints on transmission and storage for single entangled systems. The deterministic preparation of entangled states is one of the key factors for the realization of quantum networks. There is no efficient method to verify whether single multipartite entanglement can be prepared by multisource quantum networks. Here, we theoretically analyze under what conditions entangled states can be prepared in three kinds of basic Gaussian quantum networks, named triangle networks, star-shaped networks, and chain-type networks. Some necessary criteria are derived for all preparable entangled Gaussian states in such networks. They show that the network structure imposes strong constraints on the set of preparable entangled Gaussian states, which is fundamentally different from standard single multipartite entanglement. This study takes the first step towards understanding the network mechanism for preparing entangled Gaussian states.