Generating nonclassical correlations without fully aligning measurements

Abstract

We investigate the scenario where spatially separated parties perform measurements in randomly chosen bases on an N-partite Greenberger-Horne-Zeilinger state. We show that without any alignment of the measurements, the observers will obtain correlations that violate a Bell inequality with a probability that rapidly approaches 1 as N increases and that this probability is robust against noise. We also prove that restricting these randomly chosen measurements to a plane perpendicular to a common direction will always generate correlations that violate some Bell inequality. Specifically, if each observer chooses their two measurements to be locally orthogonal, then the N observers will violate one of two Bell inequalities by an amount that increases exponentially with N. These results are also robust against noise and perturbations of each observer's reference direction from the common direction.

v2: Essentially published version (with typos fixed, results updated in Table 2 and Figure 4 replaced); v1: 16 pages, 5 figures, 2 tables, comments welcome

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• Nonlocality of $W$ and Dicke states subject to losses
• Anonymous Quantum Nonlocality
• Survey on the Bell nonlocality of a pair of entangled qudits
• Demonstrating genuine multipartite entanglement and nonseparability without shared reference frames
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• Device-Independent Bounds on Detection Efficiency
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• Experimentally friendly approach towards nonlocal correlations in multisetting N -partite Bell scenarios
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• Random constructions in Bell inequalities: A survey
• Analytic quantification of the singlet nonlocality for the first Bell's inequality
• Bell tests with random measurements require very high detection efficiencies