Optimizing and Certifying Multipartite Permutationally Invariant Bell Inequalities

Jin-Fu Chen; Mengyao Hu; Jordi Tura

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arXiv · 2607.08462

Optimizing and Certifying Multipartite Permutationally Invariant Bell Inequalities

Jin-Fu Chen·Mengyao Hu·Jordi Tura

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Abstract

Multipartite Bell nonlocality provides a device-independent probe of many-body quantum correlations, but its characterization is limited by the rapid growth of the underlying classical and quantum optimization problems. We develop a scalable method for constructing and certifying permutationally invariant Bell inequalities using only one- and two-body correlators. The construction gives families of inequalities with robust quantum violations for general $m$ measurements as the number of parties $N$ becomes large. To improve robustness against noise, we optimize the ratio of the quantum value to the classical bound for these families in the large-$N$ limit. We then certify the resulting quantum violation using semidefinite programming. For the broad class of Bell inequalities studied here, the infinite-$N$ ratios take simple rational values for finite $m$ and converge to $\coth(1)$ as $m\to\infty$. The optimized inequalities efficiently detect many-body Bell nonlocality with collective measurements, with more measurement settings leading to stronger violations.

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Jin-Fu Chen, Mengyao Hu, Jordi Tura. 2026-07-09. Optimizing and Certifying Multipartite Permutationally Invariant Bell Inequalities. https://arxiv.org/abs/2607.08462

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