Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities

TL;DR

This paper introduces an efficient method for constructing noncontextual polytopes, enabling the discovery of new inequalities and applications in quantum certification and randomness, regardless of measurement complexity.

Contribution

The work develops a scalable approach to compute noncontextual polytopes with fixed preparation dimension, facilitating the exploration of quantum contextuality scenarios.

Findings

Uncovered new noncontextuality inequalities.

Demonstrated quantum contextual correlations in measurement certification.

Showcased applications in system dimension witnessing and randomness certification.

Abstract

Finding a set of empirical criteria fulfilled by any theory satisfying the generalized notion of noncontextuality is a challenging task of both operational and foundational importance. This work presents a methodology for constructing the noncontextual polytope while ensuring that the dimension of the polytope associated with the preparations remains constant regardless of the number of measurements and their outcome size. The facet inequalities of the noncontextual polytope can thus be obtained in a computationally efficient manner. We illustrate the efficacy of our methodology through several distinct contextuality scenarios. Our investigation uncovers several hitherto unexplored noncontextuality inequalities and demonstrates applications of quantum contextual correlations in certification of non-projective measurements, witnessing the dimension of quantum systems, and randomness certification.