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arXiv · 2203.16543

Proofs of network quantum nonlocality in continuous families of distributions

Alejandro Pozas-Kerstjens·Nicolas Gisin·Marc-Olivier Renou
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Abstract

The study of nonlocality in scenarios that depart from the bipartite Einstein-Podolsky-Rosen setup is allowing to uncover many fundamental features of quantum mechanics. Recently, an approach to building network-local models based on machine learning lead to the conjecture that the family of quantum triangle distributions of [arXiv:1905.04902] did not admit triangle-local models in a larger range than the original proof. We prove part of this conjecture in the affirmative. Our approach consists in reducing the family of original, four-outcome distributions to families of binary-outcome ones, and then using the inflation technique to prove that these families of binary-outcome distributions do not admit triangle-local models. This constitutes the first successful use of inflation in a proof of quantum nonlocality in networks whose nonlocality could not be proved with alternative methods. Moreover, we provide a method to extend proofs of network nonlocality in concrete distributions of a parametrized family to continuous ranges of the parameter. In the process, we produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.

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Alejandro Pozas-Kerstjens, Nicolas Gisin, Marc-Olivier Renou. 2022-03-30. Proofs of network quantum nonlocality in continuous families of distributions. https://doi.org/10.1103/physrevlett.130.090201

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