Combining contextuality and causality: a game semantics approach.

We develop an approach to combining contextuality with causality, which is general enough to cover causal background structure, adaptive measurement-based quantum computation and causal networks. The key idea is to view contextuality as arising from a game played between Experimenter and Nature, allowing for causal dependencies in the actions of both the Experimenter (choice of measurements) and Nature (choice of outcomes). This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

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

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 between information sources. This result vastly generalizes previously observed connections between contextuality, relat- ional 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.

A complete characterization of all-versus-nothing arguments for stabilizer states.

An important class of contextuality arguments in quantum foundations are the all-versus-nothing (AvN) proofs, generalizing a construction originally due to Mermin. We present a general formulation of AvN arguments and a complete characterization of all such arguments that arise from stabilizer states. We show that every AvN argument for an -qubit stabilizer state can be reduced to an AvN proof for a three-qubit state that is local Clifford-equivalent to the tripartite Greenberger-Horne-Zeilinger state.

Contextual Fraction as a Measure of Contextuality.

We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e., tables of probabilities of measurement outcomes in an experimental scenario.