Translationally invariant multipartite Bell inequalities involving only two-body correlators

J. Tura, A. B Sainz, T. Vértesi, A. Acín, M. Lewenstein, R. Augusiak

Research output: Contribution to journalArticle

14 Citations (Scopus)

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 languageEnglish
Article number424024
JournalJournal of Physics A: Mathematical and Theoretical
Volume47
Issue number42
DOIs
Publication statusPublished - Oct 24 2014

Fingerprint

Bell's Inequality
Correlators
Correlator
correlators
bells
Nonlocality
Invariant
Translational symmetry
Quantum State
Numerical Algorithms
Quantum Systems
Correlation Function
Observer
Nearest Neighbor
Physics
theorems
physics
Theorem
symmetry
Demonstrate

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

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

In: Journal of Physics A: Mathematical and Theoretical, Vol. 47, No. 42, 424024, 24.10.2014.

Research output: Contribution to journalArticle

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