Beyond Bell's theorem: correlation scenarios

By Tobias Fritz. 2012

269 citations recorded by the source corpus.

Bell's theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard, Rosset, Gisin and Pironio, we consider scenarios which feature several sources, but no choice of measurement for the observers. Every Bell scenario can be mapped into such a correlation scenario, and Bell's theorem then discards those local hidden variable theories in which the sources are independent. However, most correlation scenarios do not arise from Bell scenarios, and we describe examples of (quantum) non-locality in some of these scenarios, while posing many open problems along the way. Some of our scenarios have been considered before by mathematicians in the context of causal inference.

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

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Citations in the corpus

Quantum common causes and quantum causal models (2016, background): “Preliminary work more directly pertaining to quantum causal models took the form of explorations of Bell-type inequalities (and whether they admit quantum violations) for novel causal scenarios [60,61].”
Margins of discrete Bayesian networks (2015, result): “estriction to pairwise independent latent parents will sometimes introduce additional inequality constraints. The marginal model for the mDAG in Figure 7(b) is strictly smaller than the one for 7(a) (Fritz, 2012, Proposition 2.13), for example. See Evans (2016) for a more detailed discussion. It fol”
Causal Inference via Algebraic Geometry: Feasibility Tests for Functional Causal Structures with Two Binary Observed Variables (2015, background): “It has recently been noted [13, 14] that one can understand the assumptions required to derive a Bell inequality as the standard assumptions for causal inference together with a particular hypothesis about the underlying causal structure, namely, that each local outcome depends causally on the…”
Theory-independent limits on correlations from generalized Bayesian networks (2014, background): “ard, Gisin and Pironio [7] found that including the independence of multiple sources could lead to more robust experiments than the single source assumption of a Bell scenario. Using this idea, Fritz [18] showed that the ‘free will’ assumption of Bell’s theorem can be replaced with an assumption abo”