### 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.

Original language | English |
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Article number | 022110 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 83 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 Feb 28 |

### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*83*(2), [022110]. https://doi.org/10.1103/PhysRevA.83.022110