Non-locality, contextuality and valuation algebras: a general theory of disagreement

Abstract

We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these peculiar features of quantum theory are mathematically equivalent to a general notion of \emph{disagreement} between information sources. This result vastly generalises previously observed connections between contextuality, relational databases, constraint satisfaction problems, and logical paradoxes, and gives further proof that contextual behaviour is not a phenomenon limited to quantum physics, but pervades various domains of mathematics and computer science. The connection allows to translate theorems, methods and algorithms from one field to the other, and paves the way for the application of generic inference algorithms to study contextuality.

arXiv comment21 pages, 3 figures

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Cited by in corpus (6)

• Observers of quantum systems cannot agree to disagree
• The Sheaf-Theoretic Structure of Definite Causality
• Closing Bell: Boxing black box simulations in the resource theory of contextuality
• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality
• Contextuality in distributed systems
• Trace models of concurrent valuation algebras