Multipartite Einstein-Podolsky-Rosen steering sharing with separable states

The distribution of quantum correlations among remote users is a key procedure underlying many quantum information technologies. Einstein-Podolsky-Rosen steering, which is one kind of such a correlation stronger than entanglement, has been identified as a resource for secure quantum networks. We show that this resource can be established between two and even more distant parties by transmission of a system being separable from all the parties. For two-user scenarios, we design a protocol allowing one to distribute one-way Gaussian steering which can be used subsequently for one-sided device-independent (1sDI) quantum key distribution. Further, we extend the protocol to three-user scenarios to distribute richer steerability properties including one-to-multimode steering and collective steering which can be used for 1sDI quantum secret sharing. All the proposed protocols can be implemented with squeezed states, beam splitters, and displacements, and thus they can be readily realized experimentally. Our findings reveal that not only entanglement but even steering can be distributed via communication of a separable system. Viewed from a different perspective, the present protocols also demonstrate that one can switch multipartite states between different steerability classes by operations on parts of the states.