Driven optomechanical systems for mechanical entanglement distribution

We consider the distribution of entanglement from a multimode optical driving source to a network of remote and independent optomechanical systems. By focusing on the tripartite case, we analyse the effects that the features of the optical input states have on the degree and sharing structure of the distributed, fully mechanical, entanglement. This study, which is conducted looking at the mechanical steady state, highlights the structure of the entanglement distributed among the nodes and determines the relative efficiency between bipartite and tripartite entanglement transfer. We discuss a few open points, some of which are directed towards the bypassing of such limitations.