Polynomial Bell Inequalities

Chaves, Rafael

doi:10.1103/physrevlett.116.010402

Cited by 139 publications

(173 citation statements)

References 61 publications

(98 reference statements)

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“…This allows us to violate the bilocal causality inequality proposed in ref. 19 and further developed in refs 20, 22, 23, 24, 25:…”

Section: Resultsmentioning

confidence: 99%

“…1c), which introduce additional structure to the set of classically allowed correlations. In fact, there are quantum correlations that can emerge in networks that, while admitting a LHV description, are incompatible with any classical description where the independence of the sources is considered19202122232425. For instance, a network with two independent sources allow for the emergence of a different kind of non-local correlations violating the so-called bilocal causality assumption1920.…”

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Experimental violation of local causality in a quantum network

et al. 2017

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Bell's theorem plays a crucial role in quantum information processing and thus several experimental investigations of Bell inequalities violations have been carried out over the years. Despite their fundamental relevance, however, previous experiments did not consider an ingredient of relevance for quantum networks: the fact that correlations between distant parties are mediated by several, typically independent sources. Here, using a photonic setup, we investigate a quantum network consisting of three spatially separated nodes whose correlations are mediated by two distinct sources. This scenario allows for the emergence of the so-called non-bilocal correlations, incompatible with any local model involving two independent hidden variables. We experimentally witness the emergence of this kind of quantum correlations by violating a Bell-like inequality under the fair-sampling assumption. Our results provide a proof-of-principle experiment of generalizations of Bell's theorem for networks, which could represent a potential resource for quantum communication protocols.

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“…This allows us to violate the bilocal causality inequality proposed in ref. 19 and further developed in refs 20, 22, 23, 24, 25:…”

Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Experimental violation of local causality in a quantum network

et al. 2017

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“…This triggered further research, with the derivation of novel non-linear inequalities and the exploration of more sophisticated networks; see e.g. [19][20][21][22][23][24][25][26][27]. However, the extent of quantum correlations in networks remains poorly understood.…”

Section: Arxiv:170200333v1 [Quant-ph] 1 Feb 2017mentioning

confidence: 99%

All entangled pure quantum states violate the bilocality inequality

et al. 2017

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The nature of quantum correlations in networks featuring independent sources of entanglement remains poorly understood. Here, focusing on the simplest network of entanglement swapping, we start a systematic characterization of the set of quantum states leading to violation of the so-called "bilocality" inequality. First, we show that all possible pairs of entangled pure states can violate the inequality. Next, we derive a general criterion for violation for arbitrary pairs of mixed twoqubit states. Notably, this reveals a strong connection between the CHSH Bell inequality and the bilocality inequality, namely that any entangled state violating CHSH also violates the bilocality inequality. We conclude with a list of open questions.

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“…Recently, there has been much interest in deriving bounds on the correlations achievable in classical causal models [76,77,79,80] using insights from the literature on Bell's theorem. Such bounds constitute Bell-like inequalities for arbitrary causal structures.…”

Section: Discussionmentioning

confidence: 99%

Causality in the Quantum World

Pienaar¹

2017

Physics

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Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach's principle would seem to demand. Motivated by this, we introduce a quantum counterpart to the principle. We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C, then it must factorize in a particular way. Finally, we show how to generalize our quantum version of Reichenbach's principle to a formalism for quantum causal models and provide examples of how the formalism works.

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Polynomial Bell Inequalities

Cited by 139 publications

References 61 publications

Experimental violation of local causality in a quantum network

Experimental violation of local causality in a quantum network

All entangled pure quantum states violate the bilocality inequality

Causality in the Quantum World

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