Production and uses of hyper-entangled states

Entangled states are central 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 discussed extensively, much less investigated experimentally. In particular, efforts to date have focussed 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 polarization, momentum-direction, and energy. 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.