More non-locality in the three-qubit Greenberger-Horne-Zeilinger state

Abstract

The non-local properties of the noisy three-qubit Greenberger-Horne-Zeilinger (GHZ) states parameterized by the visibility 0<v<1 are investigated. Based on the violation of the 2x2x2-setting Mermin inequality, the noisy three-qubit GHZ states are non-local for the parameter range 1/2<v<1. It has been posed whether additional settings would allow to lower the threshold visibility. Here we report on Bell inequalities giving a threshold value smaller than v=1/2. This rules out the possibility of a local hidden variable model in the limit of v=1/2. In particular, the lowest threshold visibility we found is v=0.496057, attainable with 5x5x5 settings, whereas the most economical one in number of settings corresponds to 3x3x4 settings. The method which enabled us to obtain these results, and in particular the about 10000 tight Bell inequalities giving v<1/2 are also discussed in detail.

8 pages, 5 tables

References in corpus (7)

• Device-independent security of quantum cryptography against collective attacks
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• More efficient Bell inequalities for Werner states
• Quantifying the nonlocality of GHZ quantum correlations by a bounded communication simulation protocol
• Necessary and sufficient detection efficiency for the Mermin inequalities
• Non-classicality thresholds for multiqubit states - numerical analysis

Cited by in corpus (6)

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• Improved local models and new Bell inequalities via Frank-Wolfe algorithms
• N-particle nonclassicality without N-particle correlations
• Optimal tests of genuine multipartite nonlocality
• Macroscopic Schrödinger Cat Resistant to Particle Loss and Local Decoherence