Corrected Bell and non-contextuality inequalities for realistic experiments.

Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a non-classical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden variables, for which it forces a contradiction with the assumptions of parameter-independence and determinism.

Quantum Advantage from Sequential-Transformation Contextuality.

We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong sequential-transformation contextuality is necessary and sufficient for deterministic computation of nonlinear functions if classical components are restricted to mod2 linearity and matching constraints apply to any underlying ontology. For probabilistic computation, sequential-transformation contextuality is necessary and sufficient for advantage in this task and the degree of advantage quantifiably relates to the degree of contextuality.

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.