2017
DOI: 10.1103/physrevlett.119.170403
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Bell Correlations in a Many-Body System with Finite Statistics

Abstract: A recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this Letter, we address here the question of the statistics required to witness Bell correlated states, i.e., states violating a Bell inequality, in such experiments. We start by deriving multipartite Bell inequalities involving an arbitrary number of measurement settings, two outcomes per party and one-and two-body correlators only. Based on these inequalitie… Show more

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Cited by 25 publications
(26 citation statements)
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“…Recently, such a reduction in the number of measurements, applicable when assuming that the measurements are known and trusted, was used to transform a Bell inequality involving an unbounded number of settings into a witness with only two global measurements [3]. It was also used to show that the Svetlichny inequality [22], which is a Bell inequality for N parties requiring the measurement of 2 N correlators, reduces to a negativity condition on the mean value of an observable that can be evaluated with 2 measurement settings only [7].…”
Section: Bell Inequalities and Bell-correlation Witnessesmentioning
confidence: 99%
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“…Recently, such a reduction in the number of measurements, applicable when assuming that the measurements are known and trusted, was used to transform a Bell inequality involving an unbounded number of settings into a witness with only two global measurements [3]. It was also used to show that the Svetlichny inequality [22], which is a Bell inequality for N parties requiring the measurement of 2 N correlators, reduces to a negativity condition on the mean value of an observable that can be evaluated with 2 measurement settings only [7].…”
Section: Bell Inequalities and Bell-correlation Witnessesmentioning
confidence: 99%
“…Exceptions have been found recently. In particular [2][3][4], showed that some multi-partite states are able to violate Bell inequalities using the product of two local observables. These inequalities paved the way for Bell tests with many-body systems where few-body correlations-correlations between a small number of local observables-are accessible only.…”
Section: Introductionmentioning
confidence: 99%
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“…It turns out that these results can be improved by considering a multi-setting generalization of the Bell inequality (8) presented in Ref. [28]. Again, this inequality can be written as a Bell correlation witness which requires collective spin measurements only.…”
Section: Bell Operators From a Qfi Boundmentioning
confidence: 99%
“…First, we take its elements to start with an ansatz for a Bell inequality, which turns out to be of the form of multipartite Bell inequalities based on two-body correlators recently introduced by Tura et al [27]. Considering a multi-setting extension of this Bell inequality [28], we show that (i) only quantum states with F(ρ, A) > N (i.e. beating the standard limit of separable states) can potentially violate the inequality, and (ii) any quantum state with F(ρ, A) > 3N will violate the Bell inequality.…”
Section: Introductionmentioning
confidence: 99%