Efficient hyperentanglement concentration for N-particle Greenberger–Horne–Zeilinger state assisted by weak cross-Kerr nonlinearity

In this scheme, based on the weak cross-Kerr nonlinearity, an hyperconcentration protocol for the arbitrary partially hyperentangled N-particle Greenberger–Horne–Zeilinger (GHZ) state is presented. Considering the N photons initially in the nonmaximally hyperentangled GHZ state in which photons are entangled simultaneously in the polarization and the spatial-mode degrees of freedom, we can obtain the maximally hyperentangled N-particle GHZ state by the projection measurements on the additional photons. Numerical simulation demonstrates that by iterating the entanglement concentration process, we can improve the success probability of the scheme. Furthermore, we discuss the feasibility of the setups of the protocol, concluding that the present protocol is feasible with existing experimental technology. All these advantages make this scheme more efficient and more convenient in quantum communication.