Direct conversion of a three-atom W state to a Greenberger-Horne-Zeilinger state in spatially separated cavities

State conversion between the Greenberger-Horne-Zeilinger (GHZ) state and the W state is a challenging open problem because these states cannot be converted to each other by just local operations and classical communication. Here we propose a cavity quantum electrodynamics method based on interference of polarized photons emitted by the atoms trapped in spatially separated optical cavities that can convert a three-atom W state to a GHZ state. We calculate the success probability and fidelity of the converted GHZ state when the cavity decay, spontaneous atomic decay and photon leakage of the cavities are taken into account for a practical system, which shows that the proposed scheme is feasible and within the reach of current experimental technology.