Reexamination of a multisetting Bell inequality for qudits

Liang, Yeong-Cherng; Lim, Chu Wee; Deng, Dong Ling

doi:10.1103/physreva.80.052116

Cited by 48 publications

(73 citation statements)

References 60 publications

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“…An equivalent inequality with the same properties was found in Refs. [32,33]. We can apply the same strategy for four qutrits starting with the GHZ state |GHZ 3 4 = (|0000 + |1111 + |2222 )/ √ 3.…”

Section: A Bell Inequalities From Entangled Statesmentioning

confidence: 99%

Operational approach to Bell inequalities: Application to qutrits

et al. 2016

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In this work we develop two methods to construct Bell inequalities for multipartite systems. By considering non-hermitian operators we study Bell inequalities for the cases of three settings, three outcomes and three to six parties. The maximal value achieved in the framework of quantum theory is computed for subsystems with three levels each. The other technique, based on a mapping from pure entangled states to Bell operators, allows us to construct further multipartite Bell inequalities. As a consequence, we reproduce some known results in a novel way and find some multipartite Bell inequalities for systems having three settings and three outcomes per party.

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Section: A Bell Inequalities From Entangled Statesmentioning

confidence: 99%

Operational approach to Bell inequalities: Application to qutrits

et al. 2016

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“…It is done the same way as in our previous method [13]. An algorithm applying this very third step has been also used by Liang et al [29] to compute quantum optima for multiple-outcome Bell expressions. From Eq.…”

Section: The Iterative Algorithmmentioning

confidence: 99%

Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems

2010

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The I3322 inequality is the simplest bipartite two-outcome Bell inequality beyond the ClauserHorne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems, however, there is no such evidence for the I3322 inequality. In this paper a family of measurement operators and states is given which enables us to attain the largest possible quantum value in an infinite dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite dimensional quantum systems is not enough to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role to obtain our results for the I3322 inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.

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“…(27) Notice that this Bell inequality separates L from Q as it is straightforward to find that the maximal value of G(Φ can be found in [35].…”

Section: Tsirelson Bounds and Bipartite Maximally Entangled Statesmentioning

confidence: 99%

Simple conditions constraining the set of quantum correlations

Vicente

2015

Phys. Rev. A

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The characterization of the set of quantum correlations in Bell scenarios is a problem of paramount importance for both the foundations of quantum mechanics and quantum information processing in the device-independent scenario. However, a clear-cut (physical or mathematical) characterization of this set remains elusive and many of its properties are still unknown. We provide here simple and general analytical conditions that are necessary for an arbitrary bipartite behaviour to be quantum. Although the conditions are not sufficient, we illustrate the strength and non-triviality of these conditions with a few examples. Moreover, we provide several applications of this result: we prove a quantitative separation of the quantum set from extremal nonlocal no-signaling behaviours in several general scenarios, we provide a relation to obtain Tsirelson bounds for arbitrary Bell inequalities and a construction of Bell expressions whose maximal quantum value is attained by a maximally entangled state of any given dimension.

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Reexamination of a multisetting Bell inequality for qudits

Cited by 48 publications

References 60 publications

Operational approach to Bell inequalities: Application to qutrits

Operational approach to Bell inequalities: Application to qutrits

Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems

Simple conditions constraining the set of quantum correlations

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