  We experimentally demonstrate the first quantum system entangled in every
degree of freedom (hyperentangled). Using pairs of photons produced in
spontaneous parametric downconversion, we verify entanglement by observing a
Bell-type inequality violation in each degree of freedom: polarization, spatial
mode and time-energy. We also produce and characterize maximally hyperentangled
states and novel states simultaneously exhibiting both quantum and classical
correlations. Finally, we report the tomography of a 2x2x3x3 system
(36-dimensional Hilbert space), which we believe is the first reported photonic
entangled system of this size to be so characterized.
