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ACTA PHOTONICA SINICA

Experimental Investigation of Entanglement and Bell-type Inequality of Generalized Greenberger-Horne-Zeilinger States

赵加强 ZHAO Jia-qiang, 曹连振 CAO Lian-zhen, Lu Huai-Xin, 王晓芹 WANG Xiao-Qin

Published Jan 1, 2014• 0 citations
Publisher

Abstract

利用制备的三光子偏振广义Greenberger-Horne-Zeilinger纠缠态，测量了三体纠缠度、Svetlichny不等式和广义Greenberger-Horne-Zeilinger态的密度矩阵．根据密度矩阵计算了三体纠缠度，测量得到了广义Greenberger-Horne-Zeilinger纠缠态的纠缠和非定域性之间的关系．结果表明：在实验误差范围内，三体纠缠度的实验测量值和理论值一致；Svetlichny算符的期望值和理论计算结果具有较好的一致性；体系非定域特性和体系的纠缠程度密切相美，当纠缠麽减小时，非定域性减弱．

DOI
10.3788/gzxb201443.0127002

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利用制备的三光子偏振广义Greenberger-Horne-Zeilinger纠缠态，测量了三体纠缠度、Svetlichny不等式和广义Greenberger-Horne-Zeilinger态的密度矩阵．根据密度矩阵计算了三体纠缠度，测量得到了广义Greenberger-Horne-Zeilinger纠缠态的纠缠和非定域性之间的关系．结果表明：在实验误差范围内，三体纠缠度的实验测量值和理论值一致；Svetlichny算符的期望值和理论计算结果具有较好的一致性；体系非定域特性和体系的纠缠程度密切相美，当纠缠麽减小时，非定域性减弱．
量纠纷是为量信息处理的一个必要资源，为量通讯或为量计算。纠纷的多国参加的盒子，特别所谓的真多国参加的纠纷，为多国参加的量信息协议有重要重要性。因此，当执行许多量信息任务时，试验性地验证多国参加的量纠纷是一个自然要求。然而，这由于在所有深奥聚会之中造一个分享的参考框架的困难经常是技术上挑战性的，特别当这些聚会离对方远时。在这份报纸，没有分享的参考书框架，我们试验性地验证一个三光子的 Greenberger-Horne-Zeilinger 状态的真分成三部分的纠纷。高可能性当没有参考书框架被分享时，成功地验证真分成三部分的纠纷中的 0.79 个被完成。在分享仅仅一普通的轴的情况中， 0.91 的甚至更高的成功可能性被完成。
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.
Based on Clauser-Horne-Shimony-Holt inequality, we show a fruitful method to exploit Bell inequalities for multipartite qubit systems. These Bell inequalities are designed with a simpler architecture tailored to experimental demonstration. With the point of view of the stabilizer formalism, we suggest a method to investigate quantum nonlocality for multipartite systems. Under the optimal setting we derive a set of compact Mermin-type inequalities and then discuss quantum violations for generalized Greenberger-Horne-Zeilinger (GGHZ) states and two kinds of mixed states. Also, as an example, we reveal relationship between quantum nonlocality and four-partite entanglement for four-qubit GGHZ states.
We analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for three-qubit pure states in the Greenberger-Horne-Zeilinger class. We consider a family of states known as the generalized Greenberger-Horne-Zeilinger states and derive an analytical expression relating the three-tangle, which quantifies tripartite entanglement, to the Svetlichny inequality, which is a Bell-type inequality that is violated only when all three qubits are nonlocally correlated. We show that states with three-tangle less than 1/2 do not violate the Svetlichny inequality. On the other hand, a set of states known as the maximal slice states does violate the Svetlichny inequality, and exactly analogous to the two-qubit case, the amount of violation is directly related to the degree of tripartite entanglement. We discuss further interesting properties of the generalized Greenberger-Horne-Zeilinger and maximal slice states.