Polynomial Bell Inequalities

Physical Review Letters
Rafael Chaves

Abstract

It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell net...Continue Reading

References

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Citations

Dec 12, 2017·Proceedings. Mathematical, Physical, and Engineering Sciences·Mirjam Weilenmann, Roger Colbeck
Mar 17, 2017·Nature Communications·Gonzalo CarvachoFabio Sciarrino
Jan 30, 2018·Physical Review Letters·Ciarán M Lee, Matty J Hoban
Apr 26, 2018·Physical Review Letters·Ming-Xing Luo
Apr 26, 2018·Physical Review Letters·R V NeryL Aolita
May 15, 2020·Nature Communications·Nicolas GisinNicolas Brunner
Jul 2, 2016·Physical Review Letters·Rafael Chaves, Costantino Budroni
May 17, 2017·Science Advances·Dylan J SaundersGeoff J Pryde
Nov 9, 2019·Physical Review Letters·Alejandro Pozas-KerstjensAntonio Acín
Sep 7, 2019·Physical Review Letters·Marc-Olivier RenouNicolas Brunner
Jan 23, 2016·Physical Review Letters·Denis RossetNicolas Gisin
Sep 26, 2020·Physical Review Letters·Johan ÅbergRafael Chaves
Jun 8, 2019·Physical Review Letters·Askery CanabarroRafael Chaves
May 20, 2020·Nature Communications·Davide PoderiniFabio Sciarrino
Dec 19, 2020·Physical Review Letters·Mariami GachechiladzeRafael Chaves
Jun 22, 2021·Physical Review Letters·Armin TavakoliCyril Branciard

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