title: Unifying framework for relaxations of the causal assumptions in Bell's theorem.
abstract: 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.
authors.affiliation: Institute for Physics, University of Freiburg, Rheinstrasse 10, D-79104 Freiburg, Germany.
authors.forename: R
authors.initials: R
authors.lastname: Chaves
authors.affiliation: Institute for Physics, University of Freiburg, Rheinstrasse 10, D-79104 Freiburg, Germany.
authors.forename: R
authors.initials: R
authors.lastname: Kueng
authors.affiliation: Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland.
authors.forename: J B
authors.initials: JB
authors.lastname: Brask
authors.affiliation: Institute for Physics, University of Freiburg, Rheinstrasse 10, D-79104 Freiburg, Germany.|Freiburg Center for Data Analysis and Modeling, Eckerstrasse 1, 79104 Freiburg, Germany.
authors.forename: D
authors.initials: D
authors.lastname: Gross