Deriving three-outcome permutationally invariant Bell inequalities

• URL: http://arxiv.org/abs/2406.11792v1
• Date: Mon, 17 Jun 2024 17:41:27 GMT
• Title: Deriving three-outcome permutationally invariant Bell inequalities
• Authors: Albert Aloy, Guillem Müller-Rigat, Jordi Tura, Matteo Fadel,
• Abstract summary: We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. Our work can have interesting applications in the detection of Bell correlations in paradigmatic spin-1 models, as well as in experiments with solid-state systems or atomic ensembles.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. This scenario is formalized by a Bell experiment with $N$ observers, each of which performs one out of two possible three-outcome measurements on their share of the system. As the complexity of the set of classical correlations prohibits its full characterization in this multipartite scenario, we consider its projection to a lower dimensional subspace spanned by permutationally invariant one- and two-body observables. This simplification allows us to formulate two complementary methods for detecting nonlocality in multipartite three-level systems, both having a complexity independent of $N$. Our work can have interesting applications in the detection of Bell correlations in paradigmatic spin-1 models, as well as in experiments with solid-state systems or atomic ensembles.

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