Hyper-entangled states

Entangled states are key ingredients to the new field of quantum information, including quantum dense coding, teleportation, and computation. However, only a relatively small class of entangled states has been investigated experimentally, or even discussed extensively. In particular, efforts to date have focused on two particles entangled in a single degree of freedom, for example polarization, or energy, or momentum direction. Novel phase-matching arrangements in spontaneous parametric down-conversion allow the preparation of pairs of photons that are simultaneously entangled in all of these. We shall call such a multiply-entangled state 'hyper-entangled'. In addition, an even more general state-a non-maximally entangled state-should be realizable, in which the amplitudes of the contributing terms are not equal.