Deriving three-outcome permutationally invariant Bell inequalities
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910691324067840 |
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| author | Aloy, Albert Müller-Rigat, Guillem Tura, Jordi Fadel, Matteo |
| author_facet | Aloy, Albert Müller-Rigat, Guillem Tura, Jordi Fadel, Matteo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deriving three-outcome permutationally invariant Bell inequalities Aloy, Albert Müller-Rigat, Guillem Tura, Jordi Fadel, Matteo Quantum Physics 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. |
| title | Deriving three-outcome permutationally invariant Bell inequalities |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.11792 |