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

We propose two simple and resource-economical schemes for remote preparation of four-partite atomic as well as cavity field cluster states. In the case of atomic state generation, we utilize simultaneous resonant and dispersive interactions of the two two-level atoms at the preparation station. Atoms involved in these interactions are individually pair-wise entangled into two different tri-partite GHZ states. After interaction, the passage of the atoms through a Ramsey zone and their subsequent detection completes the protocol. However, for field state generation we first copy the quantum information in the cavities to the atoms by resonant interactions and then adapt the same method as in the case of atomic state generation. The method can be generalised to remotely generate any arbitrary graph states in a straightforward manner.