Sampling Quantum Nonlocal Correlations with High Probability

González-Guillén, Carlos E.; Jimenez, Chloé; Palazuelos, Carlos; Villanueva, Ignacio

doi:10.1007/s00220-016-2625-8

Cited by 7 publications

(21 citation statements)

References 15 publications

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“…That is, given an entangled state it is very likely that one can prove its nonclassicality on a first try by choosing random observables (note also related recent results in Ref. [29]). This is to be contrasted with the original demonstration [27,28], involving two qubits, where the settings have to be carefully selected.…”

Section: All Typical States Of Five or More Qubits Violate Local Realmentioning

confidence: 99%

Multipartite nonlocality and random measurements

et al. 2017

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We present an exhaustive numerical analysis of violations of local realism by families of multipartite quantum states. As an indicator of nonclassicality we employ the probability of violation for randomly sampled observables. Surprisingly, it rapidly increases with the number of parties or settings and even for relatively small values local realism is violated for almost all observables. We have observed this effect to be typical in the sense that it emerged for all investigated states including some with randomly drawn coefficients. We also present the probability of violation as a witness of genuine multipartite entanglement.Comment: 8 pages, 2 figures, 3 tables, journal versio

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Section: All Typical States Of Five or More Qubits Violate Local Realmentioning

confidence: 99%

Multipartite nonlocality and random measurements

et al. 2017

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“…In [24] the same problem was considered from the correlation matrices point of view. That is, if one picks a quantum correlation matrix at random, which is the probability that it is nonlocal?…”

Section: Bipartite Correlation Bell Inequalitiesmentioning

confidence: 99%

“…It is well known that this is exactly the same as sampling independent normalized m-dimensional real gaussian vectors. It is very easy to see that if one fixes any finite m, the probability that a quantum correlation matrix sampled according to the previous procedure is nonlocal tends to one as N tends to infinity (see [24,Section 2] for details). However, this kind of sampling does not say too much since the set of quantum correlation matrices of order N which can be obtained with a fixed m is very small.…”

Section: Bipartite Correlation Bell Inequalitiesmentioning

confidence: 99%

Random Constructions in Bell Inequalities: A Survey

Palazuelos

2018

Found Phys

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Initially motivated by their relevance in foundations of quantum mechanics and more recently by their applications in different contexts of quantum information science, violations of Bell inequalities have been extensively studied during the last years. In particular, an important effort has been made in order to quantify such Bell violations. Probabilistic techniques have been heavily used in this context with two different purposes. First, to quantify how common the phenomenon of Bell violations is; and secondly, to find large Bell violations in order to better understand the possibilities and limitations of this phenomenon. However, the strong mathematical content of these results has discouraged some of the potentially interested readers. The aim of the present work is to review some of the recent results in this direction by focusing on the main ideas and removing most of the technical details, to make the previous study more accessible to a wide audience.

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“…The precise statement we will use is the following. A proof for it can be seen in [11], Proposition 1.5. Lemma 1.2.…”

Section: Correlation Matrices and Tensor Normsmentioning

confidence: 96%

“…One of the first steps in this direction was given in [3], where the authors study the dual question, that is: how likely is it for a random (in a certain sense) Bell inequality to attain a strictly higher value on quantum correlations than on classical correlations? Later, in [11], some of the authors of this note initiated the study of random correlations in the particular case where these correlations arise as the product of two rectangular normalized Gaussian matrices, a setting motivated by a well known result of Tsirelson that we explain below. These results, among others, are summarized in greater depth in the survey paper [17].…”

Section: Introductionmentioning

confidence: 99%

Random Quantum Correlations are Generically Non-classical

González-Guillén

Lancien

Palazuelos

et al. 2017

Ann. Henri Poincaré

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Abstract. It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically nonclassical features. In this paper we delve into a comprehensive study of random instances of such bipartite correlations. The main question we are interested in is: given a quantum correlation, taken at random, how likely is it that it is truly non-explainable by a classical model? We show that, under very general assumptions on the considered distribution, a random correlation which lies on the border of the quantum set is with high probability outside the classical set. What is more, we are able to provide the Bell inequality certifying this fact. On the technical side, our results follow from (i) estimating precisely the "quantum norm" of a random matrix, and (ii) lower bounding sharply enough its "classical norm", hence proving a gap between the two. Along the way, we need a non-trivial upper bound on the ∞→1 norm of a random orthogonal matrix, which might be of independent interest.

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Sampling Quantum Nonlocal Correlations with High Probability

Cited by 7 publications

References 15 publications

Multipartite nonlocality and random measurements

Multipartite nonlocality and random measurements

Random Constructions in Bell Inequalities: A Survey

Random Quantum Correlations are Generically Non-classical

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