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arXiv:quant-ph/0302137 · Physical Review Letters

Experimental Violation of Local Realism by Four-Photon Greenberger-Horne-Zeilinger Entanglement

Zhi Zhao, Tao Yang, Yu-Ao Chen, An‐Ning Zhang, Marek Żukowski, Jian-Wei Pan

Published Oct 28, 2003• 215 citations
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Abstract

We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.

DOI
10.1103/physrevlett.91.180401

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•Nov 13, 2002•0 citations
We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.
The highest qubit Ardehali inequality violation with 203 standard deviations is first experimentally demonstrated using the hyper-entangled four-photon-eight-qubit Greenberger-Horne-Zeilinger (GHZ) state. Moreover, we experimentally investigate the robustness of the Ardehali inequality for the four-, six-, and eight-qubit GHZ states in a rotary noisy environment systematically. Our results first validate the Ardehali' theoretical statement of relation between violation of Ardehali inequality and particle number, and proved that Ardehali inequality is more robust against noise in larger number qubit GHZ states, and provided an experimental benchmark for us to estimate the safety of quantum channel in the noisy environment.
Introduction Since its inception, fifty years ago, Bell's theorem has had a long history not only of experimental tests but also of theoretical developments. Studying pairs of correlated quantummechanical particles separated in space, in a composite “entangled” state, Bell [1] showed that the joint ascription of hidden variables and locality to the system led to an inequality that is violated by the predictions of quantum mechanics. Fifteen years later, experiments confirmed the predictions of quantum mechanics, ruling out a large class of local realist theories. One of the most meaningful theoretical developments that followed Bell's work was the Greenberger–Horne–Zeilinger (GHZ) theorem, also known as Bell's theorem without inequalities. In 1989, the American physicists Daniel Greenberger and Michael Horne, who had been working on Bell's theorem since the late 1960s, together with the Austrian physicist Anton Zeilinger, introduced a novelty into the testing of entanglement, extending Bell's theorem in a different and interesting direction. According to Franck Laloë [2], For many years, everyone thought that Bell had basically exhausted the subject by considering all really interesting situations, and that two-spin systems provided the most spectacular quantum violations of local realism. It therefore came as a surprise to many when in 1989 Greenberger, Horne, and Zeilinger (GHZ) showed that systems containing more than two correlated particles may actually exhibit even more dramatic violations of local realism. The trio analyzed the Einstein, Podolsky, and Rosen 1935 argument once again and were able to write what are now called Greenberger–Horne–Zeilinger (GHZ) entangled states, involving three or four correlated spin-1/2 particles, leading to conflicts between local realist theories and quantum mechanics. However, unlike Bell's theorem, the conflict now was not of a statistical nature, as was the case with Bell's theorem, insofar as measurements on a single GHZ state could lead to conflicting predictions with local realistic models [3–5]. In this paper we present the history of the creation of this theorem and analyze its scope.
Using the spontaneous parametric down conversion and post-selection method, we experimentally prepare the four-photon Greenberger-Horne-Zeilinger (GHZ) states with a high fidelity about 83.1%. Then, an efficiently method to improve the contrast ratio of the four-photon state is reported by theoretical analysis and experiment optimization. Based on the state, we study the local realism of this state and achieve 28 standard deviations, confirm the existence of genuine four-particle entanglement. Our work has important significance for experimental preparation and studying nonlocality of the high-fidelity multiple-photon entanglement states.
By exploiting both the photons’ polarization and spatial degrees of freedom, we experimentally demonstrate a hyper-entangled four-photon six-qubit Greenberger-Horne-Zeilinger (GHZ) state. Based on the state, we experimentally test the multi-particle Ardehali inequality and prove the theoretical prediction of Ardehali. Furthermore, we experimentally first investigate the robustness of the Ardehali inequality for the four-photon six-qubit GHZ state in a bit-flip noise environment and show the good robustness against decoherence for this inequality. Our works provide an experimental benchmark to estimate the safety of quantum channel in the noisy environment.
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.