Conditional generation of quantum entanglement of many distant atoms via multifold coincidence detection

It has been shown that there exist two inequivalent classes of three-qubit entangled states, namely, the Greenberger-Horne-Zeilinger (GHZ) class and the W class. In this paper, we propose conditional schemes to generate GHZ states and W states of three distant atoms, which are trapped separately in three leaky cavities. More generally, the schemes can be modified to generate any superposition of the Dicke states of three distant atoms. The proposed schemes require linear optical elements and a multifold coincidence detection and are insensitive to. the quantum noise. It is briefly pointed out that these schemes can be extended to generate GHZ states and W states,of N distant atoms.