### Abstract

Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making their experimental implementation difficult. The main purpose of this work is to explore the possibility of witnessing nonlocality in multipartite quantum states from the easiest-to-measure quantities, that is, the two-body correlations. In particular, we determine all three- and four-partite Bell inequalities constructed from one- and two-body expectation values that obey translational symmetry, and show that they reveal nonlocality in multipartite states. Also, by providing a particular example of a five-partite Bell inequality, we show that nonlocality can be detected from two-body correlators involving only nearest neighbours. Finally, we demonstrate that any translationally invariant Bell inequality can be maximally violated by a translationally invariant state and the same set of observables at all sites. We provide a numerical algorithm allowing one to seek for maximal violation of a translationally invariant Bell inequality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.

Original language | English |
---|---|

Article number | 424024 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 42 |

DOIs | |

Publication status | Published - Oct 24 2014 |

### Fingerprint

### Keywords

- Bell inequalities
- Bells theorem
- nonlocality

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*47*(42), [424024]. https://doi.org/10.1088/1751-8113/47/42/424024

**Translationally invariant multipartite Bell inequalities involving only two-body correlators.** / Tura, J.; B Sainz, A.; Vértesi, T.; Acín, A.; Lewenstein, M.; Augusiak, R.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 47, no. 42, 424024. https://doi.org/10.1088/1751-8113/47/42/424024

}

TY - JOUR

T1 - Translationally invariant multipartite Bell inequalities involving only two-body correlators

AU - Tura, J.

AU - B Sainz, A.

AU - Vértesi, T.

AU - Acín, A.

AU - Lewenstein, M.

AU - Augusiak, R.

PY - 2014/10/24

Y1 - 2014/10/24

N2 - Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making their experimental implementation difficult. The main purpose of this work is to explore the possibility of witnessing nonlocality in multipartite quantum states from the easiest-to-measure quantities, that is, the two-body correlations. In particular, we determine all three- and four-partite Bell inequalities constructed from one- and two-body expectation values that obey translational symmetry, and show that they reveal nonlocality in multipartite states. Also, by providing a particular example of a five-partite Bell inequality, we show that nonlocality can be detected from two-body correlators involving only nearest neighbours. Finally, we demonstrate that any translationally invariant Bell inequality can be maximally violated by a translationally invariant state and the same set of observables at all sites. We provide a numerical algorithm allowing one to seek for maximal violation of a translationally invariant Bell inequality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.

AB - Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making their experimental implementation difficult. The main purpose of this work is to explore the possibility of witnessing nonlocality in multipartite quantum states from the easiest-to-measure quantities, that is, the two-body correlations. In particular, we determine all three- and four-partite Bell inequalities constructed from one- and two-body expectation values that obey translational symmetry, and show that they reveal nonlocality in multipartite states. Also, by providing a particular example of a five-partite Bell inequality, we show that nonlocality can be detected from two-body correlators involving only nearest neighbours. Finally, we demonstrate that any translationally invariant Bell inequality can be maximally violated by a translationally invariant state and the same set of observables at all sites. We provide a numerical algorithm allowing one to seek for maximal violation of a translationally invariant Bell inequality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.

KW - Bell inequalities

KW - Bells theorem

KW - nonlocality

UR - http://www.scopus.com/inward/record.url?scp=84907855427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907855427&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/47/42/424024

DO - 10.1088/1751-8113/47/42/424024

M3 - Article

AN - SCOPUS:84907855427

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 42

M1 - 424024

ER -