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

TL;DR

This paper reveals a deep mathematical connection between quantum phenomena like non-locality and contextuality and the concept of disagreement in valuation algebras, unifying diverse areas such as physics, databases, and logic.

Contribution

It establishes a general theoretical framework linking quantum contextuality to disagreement in valuation algebras, enabling cross-disciplinary transfer of methods and algorithms.

Findings

Quantum contextuality is equivalent to disagreement in valuation algebras.

The connection generalizes links between quantum phenomena, databases, and logical paradoxes.

Enables applying inference algorithms to study contextuality.

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.