Optimizing and Certifying Multipartite Permutationally Invariant Bell Inequalities

• URL: http://arxiv.org/abs/2607.08462v1
• Date: Thu, 09 Jul 2026 13:21:09 GMT
• Title: Optimizing and Certifying Multipartite Permutationally Invariant Bell Inequalities
• Abstract summary: We develop a method for constructing and certifying permutationally invariant Bell inequalities using only one- and two-body correlators.<n>We optimize the ratio of the quantum value to the classical bound for these families in the large-$N$ limit.<n>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 $mtoinfty$.
• Score: 2.4545951785034075
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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