Enhancing the Violation of the Einstein-Podolsky-Rosen Local Realism by Quantum Hyper-entanglement

Mermin's observation [Phys. Rev. Lett. {\bf 65}, 1838 (1990)] that the magnitude of the violation of local realism, defined as the ratio between the quantum prediction and the classical bound, can grow exponentially with the size of the system is demonstrated using two-photon hyper-entangled states entangled in polarization and path degrees of freedom, and local measurements of polarization and path simultaneously.