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Zhongguo kexue. Wulixue Lixue Tianwenxue

Preparation of generalized Greenberger-Horne-Zeilinger and measurement of nonlocality

Jia Zhao

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Using spontaneous parametric down conversion and optimizing the scheme of experiment,we prepared the generalized Greenberger-Horne-Zeilinger(GGHZ) states.With over-complement quantum tomography,we achieve the density matrix and calculate the fidelity of the state as 85%±1%.Then,based on the state,we measure the expectation value of Bell-Mermin operator.In the experiment we obtained accordant result with theoretical calculation.It is show that the nonlocality of quantum states is directly related to the degree of tripartite entanglement.And the results also testify our scheme of GGHZ states and measure method of nonlocality.

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Using spontaneous parametric down conversion and optimizing the scheme of experiment,we prepared the generalized Greenberger-Horne-Zeilinger(GGHZ) states.With over-complement quantum tomography,we achieve the density matrix and calculate the fidelity of the state as 85%±1%.Then,based on the state,we measure the expectation value of Bell-Mermin operator.In the experiment we obtained accordant result with theoretical calculation.It is show that the nonlocality of quantum states is directly related to the degree of tripartite entanglement.And the results also testify our scheme of GGHZ states and measure method of nonlocality.
Using spontaneous parametric down conversion and optimizing the scheme of experiment, we prepared the generalized Greenberger-Horne-Zeilinger (GGHZ) states. With over-complement quantum tomography, we achieve the density matrix and calculate the fidelity of the state as 85%±1%. Then, based on the state, we measure the expectation value of Bell-Mermin operator. In the experiment we obtained accordant result with theoretical calculation. It is show that the nonlocality of quantum states is directly related to the degree of tripartite entanglement. And the results also testify our scheme of GGHZ states and measure method of nonlocality.
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.
As stated by S. Ghose et al. [Phys. Rev. Lett. 102, 250404 (2009)], there are certain relationships between tripartite entanglement and tripartite nonlocality for three-qubit Greenberger-Horne-Zeilinger (GHZ) class states. In the present work, we have experimentally demonstrated the theoretical results of Ghose et al. by using both three-photon generalized GHZ (GGHZ) states and maximal slice (MS) states with a count of $\ensuremath{\sim}$10/s. From the data, we have verified the agreement of the experimental violation of the Svetlichny inequality with the one predicted by quantum mechanics given the reconstructed density matrix. For the MS states, it is demonstrated that the amount of violation increases linearly following the increase of the degree of tripartite entanglement. In contrast, for GGHZ states, there is a minimal value of the violation when the degree of tripartite entanglement is 1/3. Both of the results are consist with the theoretical prediction.
We investigate experimentally the violation of the Bell, Mermin and Svetlichny inequalities to local realism prediction. Using the maximum-likelihood technique to construct the density matrix and calculate the fidelity of the Greenberger-Horne-Zeilinger (GHZ) state. The values of the three inequalities are measured. The experimental resuls show that the three inequalities have different violation degrees to local realism prediction. So we can choose a suitable method of nonlocality to estimate the security of quantum channel.
In this paper, we investigate the genuine three-way nonlocality which is recognized as the strongest form of tripartite correlations. We consider theoretically and experimentally a series of suitable Bell-type inequalities a violation of which is sufficient for the detection of three-way nonlocality. For the generalized GHZ (gGHZ) states, it is demonstrated that they do violate tripartite Bell-type inequalities for any degree of tripartite entanglement even if they do not violate Svetlichny inequality. It implies that three-way entangled gGHZ can always exhibit genuine three-way nonlocality under the requirement of time-order-dependent principle. Furthermore, we have determined the maximal amount of noise admissible for the gGHZ states to still remain genuine three-way nonlocal.