Nonlinear Bell Inequalities Tailored for Quantum Networks

Rosset, Denis; Branciard, Cyril; Barnea, Tomer Jack; Pütz, Gilles; Brunner, Nicolás; Gisin, Nicolas

doi:10.1103/physrevlett.116.010403

Cited by 140 publications

(178 citation statements)

References 27 publications

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“…Thus, we have found the violation 4 √ 2V 2 whenever V > 1/2 √ 2. The critical visibility V c = 1/2 √ 2 is the same as obtained in previous studies of correlations on this network [19,21].…”

supporting

confidence: 56%

“…Also, it is worth observing that when N is an extension of N by a two-particle source (L = 1), our inequalities reduce to those derived in Ref. [21], up to the just mentioned minor modifications.…”

supporting

confidence: 45%

“…, X M ), the local outcome of A k is determined by X k and the set of local random variables λ k to the sources of which A k is connected by receiving a part of the emitted physical system. Thus, any classical model satisfies [21];…”

mentioning

confidence: 99%

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Bell-type inequalities for arbitrary noncyclic networks

Tavakoli

2016

Phys. Rev. A

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Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers sharing some configuration of many independent physical systems. Here, we show how to construct Bell-type inequalities for correlations arising in any tree-structured network i.e. networks without cycles. This is achieved by an iteration procedure that in each step allows one to add a branch to the tree-structured network and construct a corresponding Bell-type inequality. We explore our inequalities in several examples, in all of which we demonstrate strong violations from quantum theory.Introduction.-The milstone work of John Bell showed that quantum correlations arising between spatially separated observers can break the limitations of classical physics [1]. Studies of correlations predicted by quantum theory has been a key to understanding fundamental properties of the theory and has led to applications in information processing including random number generation [2], device-independent cryptography [3] and reduction of communication complexity [4].A Bell experiment considers a source emitting a physical system shared between a set of observers who can randomly chose to apply some local measurements. The standard two-particle Bell experiment is illustrated in Figure 1 a). The properties of the correlations arising between the outcomes of the observers in Bell experiments have been thoroughly studied [5] and may be considered fairly well understood. However, much less is known about the nature of correlations arising in more sophisticated network configurations beyond the Bell experiments. A network could in general involve many independent sources each emitting a physical system that is shared between some set of observers. Importantly, a single observer could be receiving subsystems of many independent physical systems originating from different sources.There are both conceptual and applied motivations for studying classical and quantum correlations in networks. Networks naturally generalize Bell experiments which makes them conceptually attractive. Also, the notion of classical correlations on a network leads to stronger constraints than those associated to standard Bell inequalities. However, these constraints also influence the strength of quantum correlations, which makes it interesting to study their comparative strength as opposed to standard Bell inequalities. Furthermore, networks are relevant in a variety of applications involving entanglement swapping experiments [6], entanglement percolation [7] and quantum repeaters protocols [8,9]. Quantum correlations in networks are interesting for the practical implementation of large scale quantum communication networks which is arguably one of the main goals of applied quantum information.

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confidence: 56%

supporting

confidence: 45%

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Bell-type inequalities for arbitrary noncyclic networks

Tavakoli

2016

Phys. Rev. A

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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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Nonlinear Bell Inequalities Tailored for Quantum Networks

Cited by 140 publications

References 27 publications

Bell-type inequalities for arbitrary noncyclic networks

Bell-type inequalities for arbitrary noncyclic networks

All entangled pure quantum states violate the bilocality inequality

Causality in the Quantum World

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