Polynomial Bell Inequalities

Rafael Chaves
Phys. Rev. Lett. 116, 010402 – Published 7 January 2016
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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 networks.

  • Figure
  • Received 17 June 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.010402

© 2016 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsNetworks

Authors & Affiliations

Rafael Chaves

  • Institute for Physics & FDM, University of Freiburg, 79104 Freiburg, Germany and Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany

See Also

Nonlinear Bell Inequalities Tailored for Quantum Networks

Denis Rosset, Cyril Branciard, Tomer Jack Barnea, Gilles Pütz, Nicolas Brunner, and Nicolas Gisin
Phys. Rev. Lett. 116, 010403 (2016)

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Vol. 116, Iss. 1 — 8 January 2016

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