Scientific article

On the inequivalence of the CH and CHSH inequalities due to finite statistics

Published inJournal of physics. A, Mathematical and theoretical, vol. 50, no. 25, 255301
Publication date2017

Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated using a finite number of samples. Therefore the nonsignaling conditions are only approximately satisfied and the robustness of the violation depends on the chosen inequality variant. We explain that phenomenon using the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario, and propose a method to optimize the statistical robustness of a Bell inequality. In the process, we describe the finite group composed of relabeling of parties, measurement settings and outcomes, and identify correspondences between the irreducible representations of this group and properties of outcome probability distributions such as normalization, signaling or having uniform marginals.

  • Bell inequality
Citation (ISO format)
RENOU, Marc Olivier et al. On the inequivalence of the CH and CHSH inequalities due to finite statistics. In: Journal of physics. A, Mathematical and theoretical, 2017, vol. 50, n° 25, p. 255301. doi: 10.1088/1751-8121/aa6f78
Main files (1)
Article (Published version)
ISSN of the journal1751-8113

Technical informations

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