Generating nonclassical correlations without fully aligning measurements

TL;DR

This paper demonstrates that randomly chosen measurements on a GHZ state can almost certainly produce nonclassical correlations violating Bell inequalities, even without measurement alignment, and these effects are robust against noise.

Contribution

It proves that random measurement bases on GHZ states can reliably generate Bell violations without alignment, expanding understanding of quantum correlations.

Findings

High probability of Bell violation with increasing N

Bell violations persist under noise and measurement perturbations

Orthogonal measurement choices lead to exponential Bell violation growth

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.