Efficient scheme for three-photon Greenberger–Horne–Zeilinger state generation

• Create three-photon states entangled in polarization and spatial degrees of freedom.
• Use a nondestructive QND detection to distinguish the two kinds of entangled states.
• Generate a three-photon Greenberger–Horne–Zeilinger state in a noisy channel.

We propose an efficient scheme for the generation of three-photon Greenberger–Horne–Zeilinger (GHZ) state with linear optics, nonlinear optics and postselection. Several devices are designed and a two-mode quantum nondemolition detection is introduced to obtain the desired state. It is worth noting that the states which have entanglement in both polarization and spatial degrees of freedom are created in one of the designed setups. The method described in the present scheme can create a large number of three-photon GHZ states in principle. We also discuss an approach to generate the desired GHZ state in the presence of channel noise.