Generation of Hyperentangled Photon Pairs

Abstract

We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric down-conversion, 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 $2\times 2\times 3\times 3$ system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.