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Physics Letters A

Experimental investigation of tripartite entanglement and nonlocality in three-qubit generalized Greenberger–Horne–Zeilinger states

Jiaqiang Zhao, Lianzhen Cao, Xiao-Qin Wang, Huai-Xin Lu

Published Jun 19, 2012• 5 citations
Publisher
DOI
10.1016/j.physleta.2012.06.016

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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 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.
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.