Violation of a Bell inequality in two-dimensional spin-orbit hypoentangled subspaces

Based on spin-orbit coupling induced by q-plates, we present a feasible experimental proposal for preparing two-dimensional spatially inhomogeneous polarizations of light. We further investigate the quantum correlations between these inhomogeneous polarizations of photon pairs generated by spontaneous parametric down-conversion, which in essence describe the so-called hypoentanglement that is established between composite spin-orbit variables of photons. The violation of the Clauser-Horne-Shimony-Holt-Bell inequality is predicted with S=2\sqrt2 to illustrate the entangled nature of the cylindrical symmetry of spatially inhomogeneous polarizations.