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Journal of Modern Optics

Hyper-entangled states

Paul G. Kwiat

Published Nov 1, 1997• 368 citations
Publisher

Abstract

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.

DOI
10.1080/09500349708231877

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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.
Quantum entanglement is known to enable otherwise impossible feats in various communication protocols, such as quantum key distribution and super-dense coding. Here we describe efforts to further enhance the usual benefits, by incorporating quantum states that are simultaneously entangled in multiple degrees of freedom – “hyperentangled”. Via the process of spontaneous parametric down conversion, we have demonstrated photon pairs simultaneously entangled in polarization and spatial mode, and have used these to realize remote entangled state preparation, full polarization Bell-state analysis, and the highest reported capacity quantum dense coding.
Summary form only given. Entangled states of multi-particle systems are arguably the quintessential feature of quantum mechanics. In addition to their central role in discussions of nonlocal quantum correlations, they form the basis of quantum information, and enable such phenomena as quantum cryptography, quantum dense coding, teleportation, and quantum computation. Yet surprisingly, to date only a limited class of entangled states has ever been produced. Via the process of spontaneous parametric downconversion in a pair of nonlinear crystals, it is now possible to produce, with high-efficiency, pairs of photons entangled in their polarization degree of freedom. Further, we can control both the extent of entanglement and the purity of the state.
Multi-dimensional entangled states have been proven to be more powerful in some quantum information processes. Down-converted photons from spontaneous parametric down-conversion are used to engineer multi-dimensional entangled states. A kind of multi-degree multi-dimensional Greenberger–Horne–Zeilinger states can also be generated. The hyper-entangled photons are entangled in energy-time, polarization and orbital angular momentum, which is proven to be useful to increase the dimension of systems and to investigate higher-dimensional entangled states.
Summary form only given. Entangled states of multi-particle systems are arguably the quintessential feature of quantum mechanics. In addition to their central role in discussions of non-local quantum correlations, they form the basis of quantum information, and enable such phenomena as quantum cryptography, quantum dense coding, teleportation, and quantum computation. Via the process of spontaneous parametric downconversion in a pair of nonlinear crystals, it is now possible to produce, with high efficiency, pairs of photons entangled in their polarisation degree of freedom. We can also control both the extent of entanglement and the purity of the state. Density matrices for states generated by this method, and measured using tomographic techniques, are shown.
We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyper-entangled). 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 hyper-entangled 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 entangled system of this size to be so characterized.