Communications in Mathematical Physics

, Volume 341, Issue 2, pp 391–434 | Cite as

Beyond Bell’s Theorem II: Scenarios with Arbitrary Causal Structure

  • Tobias FritzEmail author


It has recently been found that Bell scenarios are only a small subclass of interesting setups for studying the non-classical features of quantum theory within spacetime. We find that it is possible to talk about classical correlations, quantum correlations and other kinds of correlations on any directed acyclic graph, and this captures various extensions of Bell scenarios that have been considered in the literature. From a conceptual point of view, the main feature of our approach is its high level of unification: while the notions of source, choice of setting and measurement all play seemingly different roles in a Bell scenario, our formalism shows that they are all instances of the same concept of “event”. Our work can also be understood as a contribution to the subject of causal inference with latent variables. Among other things, we introduce hidden Bayesian networks as a generalization of hidden Markov models.


Hide Markov Model Bayesian Network Measurable Space Conditional Distribution Directed Acyclic Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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