Hybrid entanglement swapping of photons: Creating the orbital angular momentum Bell states and Greenberger-Horne-Zeilinger states

Twisted photons offer a high-dimensional Hilbert space with the degree of freedom of orbital angular momentum (OAM). Entanglement swapping allows entangling photons that never interact. We report in this paper the hybrid entanglement swapping from multiphoton spin-entangled states to multiphoton OAM entangled states with the aid of N-pair hybrid spin-OAM entangled photons. Our scheme provides a feasible method for creating the two-photon OAM Bell states (N=2) or multiphoton multidimensional OAM Greenberger-Horne-Zeilinger states (N{>=}3). We highlight the advantage of multiparticle, multidimensional entangled states in some applications of quantum information protocols.