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arXiv:quant-ph/9810075 · Physical Review Letters

Characterizing Greenberger-Horne-Zeilinger Correlations in Nondegenerate Parametric Oscillation via Phase Measurements

William J. Munro, Gerard J Milburn

Published Nov 16, 1998• 21 citations
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Abstract

We present a potential realization of the Greenberger-Horne-Zeilinger ``all or nothing'' contradiction of quantum mechanics with local realism using phase measurement techniques in a simple photon number triplet. Such a triplet could be generated using nondegenerate parametric oscillation.
DOI
10.1103/physrevlett.81.4285

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A proposal is made for obtaining a mesoscopic realization of the Greenberger-Horne-Zeilinger (GHZ) "all or nothing" contradiction between quantum mechanics and local realism in the context of cavity QED. The proposed experiment involves three separated micromaser cavities, each initially prepared in a coherent state, which are then entangled by dispersive atom-field interactions followed by selective ionization of a single atom that has passed through all three cavities. The cavities are then probed individually by single atoms manipulated to obtain a measurement of the parity of the cavity fields. Using an isomorphism between coherent-state cavity fields and a spin-\textonehalf{} system, we show how this experiment gives rise to violations of local realism in the manner of GHZ.
It is shown that the Greenberger-Horne-Zeilinger theorem can be generalized to the case with only two entangled particles. The reasoning makes use of two photons which are maximally entangled both in polarization and in spatial degrees of freedom. In contrast to Cabello's argument of "All versus Nothing" nonlocality with four photons [Phys. Rev. Lett. 87, 010403 (2001)], our proposal to test the theorem can be implemented with linear optics and thus is well within the reach of current experimental technology.
The Greenberger-Horne-Zeilinger (GHZ) theorem exhibits an ``all versus nothing'' contradiction between Ernstein, Podelsky, and Rosen's local realism and quantum mechanics by using a maximally entangled state of three qubits. However, it is shown in this paper that no extension of GHZ's proof is possible for any entangled state of two qubits, including Bell states. The proof is obtained by showing the fact that there are no more than three distinct elements (except for a different sign) in a set of mutually commuting nonlocal spin observables of two qubits. This also leads to a generic setup of the Kochen-Specker theorem for the two-qubit system.
We present an experimental method to engineer polarization-momentum hyperentangled two-photon states, using linear optics and a single type-I nonlinear crystal. These states have been completely characterized and their nonlocal behavior has been verified by an ``all versus nothing'' test of local realism, which represents a generalization of the Greenberger-Horne-Zeilinger (GHZ) to the case of two entangled particles and two observers. The manipulation of these states may represent a useful control in quantum state engineering and Bell state measurements and, more in general, in quantum information applications.