Network nonlocality via rigidity of token counting and color matching

Renou, Marc-Olivier; Beigi, Salman

doi:10.1103/physreva.105.022408

Cited by 13 publications

(17 citation statements)

References 44 publications

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“…, f n ) defined above admits an N -compatible matrix decomposition with the minimal aforementioned assumptions on the underlying physical theory. To prove our result we need to restrict to a subclass of networks first introduced in [22].…”

Section: Resultsmentioning

confidence: 99%

Covariance Decomposition as a Universal Limit on Correlations in Networks

Beigi,

Renou

2021

Preprint

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Parties connected to independent sources through a network can generate correlations among themselves. Notably, the space of feasible correlations for a given network, depends on the physical nature of the sources and the measurements performed by the parties. In particular, quantum sources give access to nonlocal correlations that cannot be generated classically. In this paper, we derive a universal limit on correlations in networks in terms of their covariance matrix. We show that in a network satisfying a certain condition, the covariance matrix of any feasible correlation can be decomposed as a summation of positive semidefinite matrices each of whose terms corresponds to a source in the network. Our result is universal in the sense that it holds in any physical theory of correlation in networks, including the classical, quantum and all generalized probabilistic theories.

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Section: Resultsmentioning

confidence: 99%

Covariance Decomposition as a Universal Limit on Correlations in Networks

Beigi,

Renou

2021

Preprint

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“…( 2) for its definition] was proven not to admit triangle-local models [15]. The proof, based on token-counting arguments [22,23], does not resemble any connection to methods employed in standard Bell nonlocality. For this reason, it is commonly accepted as the first demonstration of genuinely quantum triangle nonlocality.…”

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confidence: 99%

Proofs of network quantum nonlocality aided by machine learning

Pozas-Kerstjens¹,

Gisin²,

Renou³

2022

Preprint

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“…One basic analytical tool is Finner's inequality [RWB + 19], that provides simple bounds on achievable correlations in non-signaling networks. In the case of classical networks, one can analytically certify the infeasibility of certain distributions based on so-called rigidity arguments [RB20]. A general possibility to further study classical, quantum or non-signaling networks is to use entropy-based outer approximations of the feasible correlations [CMG15,CB16,WC17].…”

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Outer approximations of classical multi-network correlations

Gitton¹

2022

Preprint

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We propose a framework, named the postselected inflation framework, to obtain converging outer approximations of the sets of probability distributions that are compatible with classical multi-network scenarios. Here, a network is a bilayer directed acyclic graph with a layer of sources of classical randomness, a layer of agents, and edges specifying the connectivity between the agents and the sources. A multi-network scenario is a list of such networks, together with a specification of subsets of agents using the same strategy. We furthermore show that the postselected inflation framework is mathematically equivalent to the standard inflation framework: in that respect, our results allow to gain further insights into the convergence proof of the inflation hierarchy of Navascuès and Wolfe, and extend it to the case of multi-network scenarios.

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Network nonlocality via rigidity of token counting and color matching

Cited by 13 publications

References 44 publications

Covariance Decomposition as a Universal Limit on Correlations in Networks

Covariance Decomposition as a Universal Limit on Correlations in Networks

Proofs of network quantum nonlocality aided by machine learning

Outer approximations of classical multi-network correlations

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