Work

Complexity of contextuality

Year: 2026

Type: article

Abstract: Generalized contextuality is a hallmark of nonclassical theories like quantum mechanics. Yet, three fundamental computational problems concerning its decidability and complexity remain open: first, determining the complexity of deciding if a theory admits a noncontextual ontological model; second, determining the complexity of deciding if such a model is possible for a specific dimension k ; and, third, efficiently computing the smallest such model when it exists, given that finding the smallest ontological model is NP-hard. We address the second problem by presenting an algorithm derived from a geometric formulation and its reduction to the intermediate simplex problem in computational geometry. We find that the complexity of deciding the existence of a noncontextual ontological model of dimension k is at least exponential in the dimension of the theory and at most exponential in k . This, in turn, implies that computing the smallest noncontextual ontological model is inefficient in general. Finally, we demonstrate the fundamental difference between finding the smallest noncontextual ontological model and the smallest ontological model using an explicit example wherein the respective minimum ontic sizes are five and four.

Source: Physical Review A

DOI: 10.1103/k9ls-xyps

Authors: Theodoros Yianni, Farid Shahandeh

Institution: Royal Holloway University of London

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,675

Funders: Engineering and Physical Sciences Research Council, Royal Holloway, University of London