Universal unitary gate for single-photon spin-orbit four-dimensional states

The recently demonstrated possibility of entangling opposite values of the orbital angular momentum (OAM) of a photon with its spin enables the realization of nontrivial one-photon spin-orbit four-dimensional states for quantum information purposes. Hitherto, however, an optical device that can able to perform arbitrary unitary transformations on such spin-orbit photon states has not been proposed yet. In this work we show how to realize such a "universal unitary gate" device, based only on the existing optical technology, and describe its operation. Besides the quantum information field, the proposed device may find applications wherever an efficient and convenient manipulation of the combined OAM and spin of light is required.