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arXiv:quant-ph/9905028 · Physical Review A

Experimental demonstration of Greenberger-Horne-Zeilinger correlations using nuclear magnetic resonance

Richard J. Nelson, David G. Cory, Seth Lloyd

Published Jan 10, 2000• 60 citations
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Abstract

The Greenberger-Horne-Zeilinger (GHZ) effect provides an example of quantum correlations that cannot be explained by classical local hidden variables. This paper reports on the experimental realization of GHZ correlations using nuclear magnetic resonance (NMR). The NMR experiment differs from the originally proposed GHZ experiment in several ways: it is performed on mixed states rather than pure states, and instead of being widely separated, the spins on which it is performed are all located in the same molecule. As a result, the NMR version of the GHZ experiment cannot entirely rule out classical local hidden variables. It nonetheless provides an unambiguous demonstration of the ``paradoxical'' GHZ correlations, and confirms the predictions of quantum mechanics.

DOI
10.1103/physreva.61.022106

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The Greenberger-Horne-Zeilinger (GHZ) effect provides an example of quantum correlations that cannot be explained by classical local hidden variables. This paper reports on the experimental realization of GHZ correlations using nuclear magnetic resonance (NMR). The NMR experiment differs from the originally proposed GHZ experiment in several ways: it is performed on mixed states rather than pure states, and instead of being widely separated, the spins on which it is performed are all located in the same molecule. As a result, the NMR version of the GHZ experiment cannot entirely rule out classical local hidden variables. It nonetheless provides an unambiguous demonstration of the ``paradoxical'' GHZ correlations, and confirms the predictions of quantum mechanics.
This paper shows how analogs of the Greenberger-Horne-Zeilinger experiment, which demonstrates the impossibility of certain types of local hidden-variable theories in quantum mechanics, can be performed using nuclear magnetic resonance on spins in molecules at finite temperature. Because of their microscopic nature, these experiments cannot rule out the presence of nonstandard interactions that could cause classical variables to imitate quantum variables. Instead, they are designed to reveal the peculiarly quantum-mechanical correlations on which the Greenberger-Horne-Zeilinger effect is based.
Abstract This work provides a simple approximate method of creating a Greenberger–Horne–Zeilinger (GHZ) state with high fidelity, using nuclear magnetic resonance (NMR) techniques, and reports on the decoherence process for these GHZ states, which is observed with a pair of encoder and decoder quantum circuits. The prepared GHZ states are verified by measuring the quantum correlations, which are well known as GHZ correlations. The results of the decoherence experiments, show that the GHZ states decay faster than bipartite entangled states such as Bell states by a factor of 1.3, and it appears that two different decoherence processes exist. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006
The Greenberger-Horne-Zeilinger (GHZ) version of the Einstein-Podolsky-Rosen (EPR) paradox is widely regarded as a conclusive logical argument that rules out the possibility of describing quantum phenomena within the framework of any model of local hidden variables in which the observers are free to choose their own experimental settings. In this paper, we show, however, that the GHZ argument implicitly relies on a subtle, though crucial, assumption that is not required by fundamental physical principles, and which had gone unnoticed. Namely, we note that the argument implicitly assumes the existence of an absolute angular frame of reference with respect to which the polarization properties of the hypothetical hidden configurations of the entangled particles, as well as the orientations of the measurement devices that test them, can be defined. We further note that such an absolute frame of reference may not exist if the hidden configurations of the entangled particles spontaneously break the gauge rotational symmetry. Indeed, by skipping the disputed requirement we are able to build a model of local hidden variables for the GHZ state, which complies with the 'free-will' hypothesis and reproduces the quantum mechanical predictions. Our model, thus, completes-in the EPR sense-the quantum description of the GHZ state.
The Greenberger-Horne-Zeilinger~(GHZ) version of the Einstein-Podolsky-Rosen~(EPR) paradox is widely regarded as a conclusive logical argument that rules out the possibility of describing quantum phenomena within the framework of a local and realistic model of hidden variables in which the observers are free to choose their own experimental settings. In this paper we show, however, that the GHZ argument implicitly relies on an additional crucial assumption, which is not required by fundamental physical principles and had gone unnoticed. Namely, we note that the argument implicitly assumes the existence of an absolute angular frame of reference with respect to which the polarization properties of the hypothetical hidden configurations of the entangled particles as well as the orientation of the measurement apparatus that test the system can be defined. We further note that such an absolute frame of reference would not exist if the hidden configurations of the entangled particles spontaneously break the gauge rotational symmetry. Indeed, by skipping this unnecessary additional assumption we are able to build an explicitly local and realistic model of hidden variables for the GHZ state, which complies with the 'free-will' hypothesis and reproduces the quantum mechanical predictions, and thus completes the description of the system in the EPR sense.