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

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 dir...

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Veröffentlicht in:Communications in mathematical physics Jg. 341; H. 2; S. 391 - 434
1. Verfasser: Fritz, Tobias
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2016
Schlagworte:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Directed Acyclic Graph
Bayesian Network
Conditional Distribution
Measurable Space
Hide Markov Model
ISSN:0010-3616, 1432-0916
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Zusammenfassung: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-015-2495-5