Unifying framework for relaxations of the causal assumptions in Bell's theorem.

By Rafael Chaves, Richard Kueng, Jonatan Bohr Brask, David Gross. 2014

96 citations recorded by the source corpus.

Bell's theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions-e.g., locality or measurement independence-have to be relaxed in order to allow for a classical description of such experiments. Here we develop a conceptual and computational framework for treating this problem. We employ the language of Bayesian networks to systematically construct alternative causal structures and bound the degree of relaxation using quantitative measures that originate from the mathematical theory of causality. The main technical insight is that the resulting problems can often be expressed as computationally tractable linear programs. We demonstrate the versatility of the framework by applying it to a variety of scenarios, ranging from relaxations of the measurement independence, locality, and bilocality assumptions, to a novel causal interpretation of Clauser-Horne-Shimony-Holt inequality violations.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, History and Philosophy of Science

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Citations in the corpus

Causal Inference via Algebraic Geometry: Feasibility Tests for Functional Causal Structures with Two Binary Observed Variables (2015, methodology): “…γ and η , the semi-algebraic set generated by this model is now a subset of a simplex with six vertices, [ γη ] ∈ { [00] , [01] , [10] , [11] , [20] , [21] } We now construct a causal model underlying γ and η by combining two simpler models, using the procedure described in section 4 in the…”
Quantum common causes and quantum causal models (2016, background): “Several researchers recognized that the formalism of classical causal models could provide a unifying framework in which to pose the problem of deriving Bell-type constraints, and that this framework might be extended to address the problem of deriving constraints on the correlations that can be obt”