Beyond Quantum: A New Lens for Contextuality

Operational theories, when encoded as COPE matrices, universally yield four distinct linear models-PreGPTs, GPTs, ontological models, and quasiprobabilistic models-each arising from specific factorization constraints; however, the analysis demonstrates that certain COPE matrices fail to admit a noncontextual ontological model, a class demanding particular attention to fully characterize the probabilistic structure of these theories.

Researchers have developed a unified mathematical framework to analyze the fundamental limits of predictability in any physical theory, revealing deep connections between probabilistic structure and contextuality.