  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.
