A New Hierarchy of Contextuality in Quantum Foundations

This article introduces a hierarchy of generalized contextuality, refining the traditional binary of contextual vs. non-contextual theories. Using general probabilistic theories (GPTs) as a framework, it proposes a resource theory where simulations act as free operations and introduces classical excess as a new monotone for measuring contextuality. Alongside this, the parity-oblivious multiplexing protocol serves as another monotone, offering practical ways to quantify how “contextual” a theory really is. By moving beyond a simple yes/no distinction, this hierarchy provides a more nuanced lens to compare theories, highlighting contextuality as a measurable resource for quantum information processing.