Quantum bounds for inequalities involving marginal expectation values

Wolfe, Elie; Yelin, Susanne F.

doi:10.1103/physreva.86.012123

Cited by 22 publications

(35 citation statements)

References 29 publications

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“…Holt scenario, and what we have found coincide with the results of Refs [50,51],. though there the authors have based themselves upon other methods.…”

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confidence: 93%

Concentration phenomena in the geometry of Bell correlations

et al. 2018

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Bell's theorem shows that local measurements on entangled states give rise to correlations incompatible with local hidden variable models. The degree of quantum nonlocality is not maximal though, as there are even more nonlocal theories beyond quantum theory still compatible with the nonsignalling principle. In spite of decades of research, we still have a very fragmented picture of the whole geometry of these different sets of correlations. Here we employ both analytical and numerical tools to ameliorate that. First, we identify two different classes of Bell scenarios where the nonsignalling correlations can behave very differently: in one case, the correlations are generically quantum and nonlocal while on the other quite the opposite happens as the correlations are generically classical and local. Second, by randomly sampling over nonsignalling correlations, we compute the distribution of a nonlocality quantifier based on the trace distance to the local set. With that we conclude that the nonlocal correlations can show a concentration phenomena: their distribution is peaked at a distance from the local set that increases both with the number of parts or measurements being performed.

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“…Holt scenario, and what we have found coincide with the results of Refs [50,51],. though there the authors have based themselves upon other methods.…”

supporting

confidence: 93%

Concentration phenomena in the geometry of Bell correlations

et al. 2018

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“…[32]. We identified the specific relationship between maximal violation of each Bell inequality and the entanglement of the associated quantum state.…”

Section: Discussionmentioning

confidence: 99%

“…Maximal violation of the CHSH inequality can be achieved with a two-qubit maximally entangled state, such as a Bell state. However, maximally [32].…”

Section: Introductionmentioning

confidence: 95%

“…The bounds derived in Ref. [32] for LHVM and QM are shown in Table I. The Clauser-Horne-Shimony-Holt (CHSH) inequality [3] is perhaps the most well-known Bell inequality.…”

Section: Introductionmentioning

confidence: 99%

“…[32] which have important consequences for comparing quantum correlations to those governed by local hidden-variable models. The most well-known examples of Bell inequalities and tests of nonlocality [2,3,5,21,22] achieve maximal violation using maximally entangled states, such as Bell states or Greenberger-Horne-Zeilinger (GHZ) states [21], which have unpolarized subsystems and hence zero marginal expectation values.…”

Section: Introductionmentioning

confidence: 99%

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Experimental violation of three families of Bell's inequalities

et al. 2013

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Bell's inequalities are important to our understanding of quantum foundations and critical to several quantum technologies. A recent work [E. Wolfe and S. F. Yelin, Phys. Rev. A 86, 012123 (2012)] derived three parametrized families of two-particle, two-setting Bell inequalities. These inequalities are important as they theoretically explore a larger volume of allowed quantum correlations over local hidden-variable models than previous results [A. Cabello, Phys. Rev. A 72, 012113 (2005)] by exploiting marginal, or single particle measurements. In this work we subject those predictions to experimental test using nonmaximally entangled photon pairs to optimize the expected violation. We find excellent agreement with the upper bounds predicted by quantum mechanics with violations of the limits imposed by local hidden-variable models as large as almost 30σ for the optimal parameters and a significant violation over a wide range of parameters.

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Multipartite Composition of Contextuality Scenarios

Sainz¹,

Wolfe²

2018

Found Phys

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Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how separate contextuality scenarios combine into a joint scenario. Under the premise that the the allowed probabilistic models satisfy the No Signalling principle, Foulis and Randall defined the unique possible way to compose two contextuality scenarios. When composing strictly-more than two test spaces, however, a variety of possible composition methods have been conceived. Nevertheless, all these formally-distinct composition methods appear to give rise to observationally equivalent scenarios, in the sense that the different compositions all allow precisely the same sets of classical and quantum probabilistic models. This raises the question of whether this property of invarianceunder-composition-method is special to classical and quantum probabilistic models, or if it generalizes to other probabilistic models as well, our particular focus being Q 1 models. Q 1 models are physically important since, when applied to scenarios constructed by a particular composition rule, coincide with the well-defined "Almost Quantum Correlations". In this work we see that some composition rules, however, give rise to scenarios with inequivalent allowed sets of Q 1 models. We find that the non-trivial dependence of Q 1 models on the choice of composition method is apparently an artifact of failure of those composition rules to capture the orthogonality relations given by the Local Orthogonality principle. We prove that Q 1 models satisfy invariance-undercomposition-method for all the constructive compositions protocols which do capture this notion of Local Orthogonality.

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Quantum bounds for inequalities involving marginal expectation values

Cited by 22 publications

References 29 publications

Concentration phenomena in the geometry of Bell correlations

Concentration phenomena in the geometry of Bell correlations

Experimental violation of three families of Bell's inequalities

Multipartite Composition of Contextuality Scenarios

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