Multipartite entanglement swapping and mechanical cluster states

We present a protocol for generating multipartite quantum correlations across a quantum network with a continuous-variable architecture. An arbitrary number of users possess two-mode entangled states, keeping one mode while sending the other to a central relay. Here a suitable multipartite detection is implemented, by multiple homodyne detections at the outputs of the interferometer, to conditionally generate a cluster state on the retained modes. This cluster state can be suitably manipulated by the parties and used for tasks of quantum communication in a fully optical scenario. More interestingly, the protocol can be used to create a purely-mechanical cluster state starting from a supply of optomechanical systems. We show that detecting the optical parts of optomechanical cavities may efficiently swap entanglement into their mechanical modes, creating cluster states up to five modes under suitable cryogenic conditions.