2010/12/31 by Joel J. Wallman, Yeong-Cherng Liang, Stephen D. Bartlett
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Bell's theorem #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Geometry #Inequality #Mathematical analysis #Mathematics #Noise (video) #Observer (physics) #Physics #Plane (geometry) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #State (computer science) #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreva.83.022110
published as Phys. Rev. A 83, 022110 (2011) · 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
openalex publication_date 2011/02/28 · arxiv created 2011/03/02 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.