Probabilistic and robust preparation of a GHZ-type state via atomic ensembles and linear optics

This paper proposes two simple and robust schemes to generate an atomic-ensemble Greenberger--Horne--Zeilinger-type (GHZ-type) entangled state via linear optics and single photon detection. These schemes are based on two-photon Hong--Ou--Mandel-type interference, therefore they are insensitive to the phase fluctuation. This advantage will make the realizations of these two schemes easier. One scheme can scale efficiently with the number of ensembles because of the used quantum memory. Both schemes are also robust to the noise and within the reach of current technology.