Hyperentanglement of two photons in three degrees of freedom

A six-qubit hyperentangled state has been realized by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum, and the indistinguishable emission produced by a two-crystal system operating with type I phase matching in the spontaneous parametric down conversion regime. The state has been characterized by a chained interferometric apparatus and its complete entangled nature has been tested by a witness criterion specifically presented for hyperentangled states. The experiment represents a realization of a genuine hyperentangled state with the maximum entanglement between the two particles allowed in the given ${2}^{3}\ifmmode\times\else\texttimes\fi{}{2}^{3}$ Hilbert space.