Nonlocality in many-body quantum systems detected with two-body correlators

Tura, Jordi; Augusiak, Remigiusz; Sainz, Ana Belén; Lücke, Bernd; Klempt, Carsten; Lewenstein, Maciej; Acín, Antonio

doi:10.1016/j.aop.2015.07.021

Cited by 63 publications

(147 citation statements)

References 116 publications

(226 reference statements)

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“…[22]. To simplify our considerations we have considered only those Bell inequalities that obey the translational symmetry.…”

Section: Resultsmentioning

confidence: 99%

“…For instance, Ref. [22] focuses on Bell inequalities that are invariant under any permutation of the parties (see also Ref. [21] for symmetric Bell inequalities with full correlators).…”

Section: Bell Inequalities From Two-body Correlatorsmentioning

confidence: 99%

“…However, they are also the easiest-to-measure quantities from which a Bell inequality can be constructed. It has recently been shown that such Bell inequalities are powerful enough to witness nonlocality in multipartite quantum states [22,23]. In particular, in Ref.…”

Section: Historical Background and Introductionmentioning

confidence: 99%

“…In particular, in Ref. [22] we proposed classes of permutationally invariant Bell inequalities involving only two-body correlators that detect nonlocality in multipartite quantum systems for any number of parties. The main aim of this paper is to follow the approach of [22], and search for all three-and four-partite Bell inequalities that obey a less restrictive symmetry: translational invariance.…”

Section: Historical Background and Introductionmentioning

confidence: 99%

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Translationally invariant multipartite Bell inequalities involving only two-body correlators

Tura¹,

Sainz²,

Vértesi³

et al. 2014

J. Phys. A: Math. Theor.

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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.Translationally invariant multipartite Bell inequalities involving . . . 2 Historical background and introductionHistorical background. The first quantum mechanical revolution took place in the beginning of the XXth century. Quantum mechanics was then discovered and used to describe and explain the laws of micro-world, and to predict and calculate with great precision the properties of quantum systems. The fundamental nature of quantum mechanics and its paradoxes were, of course, discussed in those times [1], but they were treated as philosophical curiosities, rather than serious scientific challenges. All of that has changed due to the seminal work of John Bell [2]. As Alain Aspect termes it, Bell's work has initiated the second quantum revolution, that has led to experimental confirmation of non-locality of quantum mechanics, pioneered by Aspect himself [3]. The same developments triggered spectacular progress of ultraprecise studies of quantum single and few particle systems, that culminated with Nobel Prizes of Hans Dehmelt, Wolfgang Paul and Norman Ramsey in 1989, and Serge Haroche and Dave Wineland in 2012. Recent developments of quantum information theory and physics of ultracold matter mark the dawn of the third quantum mechanical revolution [4]. Quantum mechanics, after achieving maturity as a physical discipline describing quantitative and fundamental aspects of the micro-world, becomes nowadays the base for future quantum technologies. The paper, that we present below, belongs to these recent trends, and treats the challenging problem of feasible detection of non-locality in many-body quantum systems.

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“…[22]. To simplify our considerations we have considered only those Bell inequalities that obey the translational symmetry.…”

Section: Resultsmentioning

confidence: 99%

“…For instance, Ref. [22] focuses on Bell inequalities that are invariant under any permutation of the parties (see also Ref. [21] for symmetric Bell inequalities with full correlators).…”

Section: Bell Inequalities From Two-body Correlatorsmentioning

confidence: 99%

Section: Historical Background and Introductionmentioning

confidence: 99%

Section: Historical Background and Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Translationally invariant multipartite Bell inequalities involving only two-body correlators

Tura¹,

Sainz²,

Vértesi³

et al. 2014

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…The presence of Bell correlations can then be probed with measurements of these collective observables alone [20,21]. This is analogous to the widely adopted entanglement depth measure for characterizing entanglement in systems with large numbers of particles [5][6][7], which makes an inference on the size of entangled clusters from measurements of collective observables.…”

mentioning

confidence: 99%