Constraints on nonlocality in networks from no-signaling and independence

Nicolas Gisin, Jean-Daniel Bancal, Yu Cai, Patrick Remy, Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Sandu Popescu, Nicolas Brunner

Research output: Contribution to journalArticle (Academic Journal)peer-review

37 Citations (Scopus)
44 Downloads (Pure)


The possibility of Bell inequality violations in quantum theory had a profound impact on our understanding of the correlations that can be shared by distant parties. Generalizing the concept of Bell nonlocality to networks leads to novel forms of correlations, the character- ization of which is, however, challenging. Here, we investigate constraints on correlations in networks under the natural assumptions of no-signaling and independence of the sources. We consider the triangle network with binary outputs, and derive strong constraints on correlations even though the parties receive no input, i.e., each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network with binary outputs.
Original languageEnglish
Article number2378
JournalNature Communications
Issue number1
Publication statusPublished - 13 May 2020

Structured keywords

  • Bristol Quantum Information Institute


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