Remote preparation of atomic and field cluster states from a pair of tri-partite GHZ states

We propose two simple and resource-economical schemes forremote preparation of four-partite atomic as well as cavity fieldcluster states. In the case of atomic state generation, we utilizesimultaneous resonant and dispersive interactions of the twotwo-level atoms at the preparation station. Atoms involved in theseinteractions are individually pair-wise entangled into two differenttri-partite GHZ states. After interaction, the passage of the atomsthrough a Ramsey zone and their subsequent detection completes theprotocol. However, for field state generation we first copy thequantum information in the cavities to the atoms by resonantinteractions and then adapt the same method as in the case of atomicstate generation. The method can be generalised to remotely generateany arbitrary graph states in a straightforward manner.