Covariance Bell inequalities

Pozsgay, Victor; Hirsch, Flavien; Branciard, Cyril; Brunner, Nicolás

doi:10.1103/physreva.96.062128

Cited by 24 publications

(16 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We can see that M(N 3 ) and M(N 4 ) are strict subsets of LM(K); both M(N 1 ) and M(N 2 ) have marginals that are not in M(N 4 ); the set M(N 4 ) consists of marginals that are not compatible with any joint PMF. • We generalize the Clauser-Horne-Shimony-Holt (CHSH) inequality [18] for Pearson correlation coefficients (PCCs), which resolves a conjecture proposed in [19].…”

Section: Contributionssupporting

confidence: 56%

Sets of Marginals and Pearson-Correlation-based CHSH Inequalities for a Two-Qubit System

Huang¹,

Vontobel²

2021

Preprint

View full text Add to dashboard Cite

Quantum mass functions (QMFs), which are tightly related to decoherence functionals, were introduced by Loeliger and Vontobel [IEEE Trans. Inf. Theory, 2017, 2020 as a generalization of probability mass functions toward modeling quantum information processing setups in terms of factor graphs.Simple quantum mass functions (SQMFs) are a special class of QMFs that do not explicitly model classical random variables. Nevertheless, classical random variables appear implicitly in an SQMF if some marginals of the SQMF satisfy some conditions; variables of the SQMF corresponding to these "emerging" random variables are called classicable variables. Of particular interest are jointly classicable variables.In this paper we initiate the characterization of the set of marginals given by the collection of jointly classicable variables of a graphical model and compare them with other concepts associated with graphical models like the sets of realizable marginals and the local marginal polytope.In order to further characterize this set of marginals given by the collection of jointly classicable variables, we generalize the CHSH inequality based on the Pearson correlation coefficients, and thereby prove a conjecture proposed by Pozsgay et al. A crucial feature of this inequality is its nonlinearity, which poses difficulties in the proof.

show abstract

Section: Contributionssupporting

confidence: 56%

Sets of Marginals and Pearson-Correlation-based CHSH Inequalities for a Two-Qubit System

Huang¹,

Vontobel²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Thus, let us define the associated n-device additive Bell parameter as: 20) and by plugging (20) into (19), we have:…”

Section: Bell and Tsirelson Bounds For The Case Of N =mentioning

confidence: 99%

Multiplicative Bell inequalities

et al. 2019

View full text Add to dashboard Cite

Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and quantum mechanical (Tsirelson) bounds for a given Bell inequality in a general scenario is a difficult task which rarely leads to closed-form solutions. Here we introduce a new class of Bell inequalities based on products of correlators that alleviate these issues. Each such Bell inequality is associated with a unique coordination game. In the simplest case, Alice and Bob, each having two random variables, attempt to maximize the area of a rectangle and the rectangle's area is represented by a certain parameter. This parameter, which is a function of the correlations between their random variables, is shown to be a Bell parameter, i.e. the achievable bound using only classical correlations is strictly smaller than the achievable bound using non-local quantum correlations We continue by generalizing to the case in which Alice and Bob, each having now n random variables, wish to maximize a certain volume in n-dimensional space. We term this parameter a multiplicative Bell parameter and prove its Tsirelson bound. Finally, we investigate the case of local hidden variables and show that for any deterministic strategy of one of the players the Bell parameter is a harmonic function whose maximum approaches the Tsirelson bound as the number of measurement devices increases. Some theoretical and experimental implications of these results are discussed.

show abstract

“…In [31] the authors present novel SOHS representation results for trace polynomials, and use them to build a converging hierarchy of SDP relaxations, which can be used to optimize over trace polynomials. The hierarchy can be practically used in the context of quantum information for finding upper bounds on quantum violations of polynomial Bell inequalities [49] and for characterizing entanglement of Werner states [28]. They also show how to extract minimizers in certain cases.…”

Section: Further Readingmentioning

confidence: 99%