Deterministic linear optical quantum Toffoli gate

Quantum Toffoli gate is a crucial part of many quantum information processing schemes. We design a deterministic linear optical quantum Toffoli gate using three degrees of freedom of a single photon. The proposed setup does not require any ancilla photons and is experimentally feasible with current technology. Moreover, we show that our setup can be directly used to demonstrate that hypergraph states violate local realism in an extreme manner.