On Tight Multiparty Bell Inequalities for Many Settings

How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given to the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.

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“…A set of multipartite three-setting Bell inequalities were studied, with two-outcome observables in Refs. [346,347]. Finally, Ref.…”

Section: Further Bell Inequalitiesmentioning

confidence: 97%

Entanglement detection

Gühne¹,

Tóth²

2009

Physics Reports

2,223

2,499

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“…Finally, a1−a3 2 is one on a = (1, 1, −1) and vanishes on a = (1, 1, 1) and on a = (1, −1, 1). One can thus see that when I 0 , I 2 and I 3 describe facets of F MN then there are 3M N linearly independent vertices of F 3MN , satisfying equation (15). Moreover, for a = (1, 1, 1), a = (1, −1, 1) and a = (1, 1, −1), the admissible vertices a ⊗ b ⊗ c satisfy I( a, b, c) ≤ 1.…”

Section: Correlation Polytope and Its Facetsmentioning

confidence: 99%

“…Given its vertices and the general form of equation ( 6), it is in general difficult to determine all the facets of the polytope [14], but for arrangements with two experimental settings per observer. With more settings per observer, one can only generate selected families of the facets and their corresponding inequalities [15,16,17].…”

Section: Correlation Polytope and Its Facetsmentioning

confidence: 99%

Clauser-Horne-Shimony-Holt-type Bell inequalities involving a party with two or three local binary settings

Badziąg

Żukowski

2009

Phys. Rev. A

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We construct a simple algorithm to generate any CHSH type Bell inequality involving a party with two local binary measurements from two CHSH type inequalities without this party. The algorithm readily generalizes to situations, where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze new symmetric inequalities for four observers and three experimental settings per observer.

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“…A method to derive mirror Bell inequalities for N qubits for three observables per site was given in Ref. [21]. Some explicit forms of such inequalities were obtained in Ref.…”

Section: Bell Inequalities Involving Only Lower Order Correlationsmentioning

confidence: 99%

N-particle nonclassicality withoutN-particle correlations

2012

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Most of known multipartite Bell inequalities involve correlation functions for all subsystems. They are useless for entangled states without such correlations. We give a method of derivation of families of Bell inequalities for N parties, which involve, e.g., only (N − 1)-partite correlations, but still are able to detect proper N -partite entanglement. We present an inequality which reveals five-partite entanglement despite using only four-partite correlations. Classes of inequalities introduced here can be put into a handy form of a single nonlinear inequality. An example is given of an N -qubit state, which strongly violates such an inequality, despite having no N -qubit correlations. This surprising property might be of potential value for quantum information tasks.

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On Tight Multiparty Bell Inequalities for Many Settings

Abstract: A derivation method is given which leads to a series of tight Bell inequalities for experiments involving N parties, with binary observables, and three possible local settings. The approach can be generalized to more settings. Ramifications are presented.

Cited by 8 publications

References 19 publications

Entanglement detection

Entanglement detection

Clauser-Horne-Shimony-Holt-type Bell inequalities involving a party with two or three local binary settings

N-particle nonclassicality withoutN-particle correlations

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