Hyperconcentration for multipartite entanglement via linear optics

We present a hyperconcentration scheme for nonlocal $N$-photon hyperentangled Greenberger-Horne-Zeilinger states. The maximally hyperentangled state, in which $N$ particles are entangled simultaneously in the polarization and the spatial mode, can be obtained with a certain probability from two partially hyperentangled states. The hyperconcentration scheme is based on one polarization parity check measurement, one spatial mode parity check measurement and N-2 single-photon two-qubit measurements. The concentration only requires linear optical elements, which makes it feasible and practical with current technology.