Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We consider classical ontological models constrained to reuse a single ontic state space across multiple interventions. We prove an information-theoretic no-go theorem showing that such models must incur an irreducible contextual information cost: contextual dependence cannot be fully mediated through the ontic state alone and requires additional contextual information beyond it. We provide a constructive example illustrating this obstruction and show that it arises solely from the requirement of ontic state reuse within a classical probability space. We further explain how quantum theory avoids this obstruction by relaxing the assumption that all measurement statistics arise from a single underlying classical ontic variable. These results identify contextuality as a fundamental information-theoretic constraint on classical ontological models and clarify its origin as a limitation on classical representations.

翻译：语境性是量子理论的核心特征，传统上被理解为无法使用非语境性本体论模型复现量子测量统计。我们考虑受限于在多重干预中重复使用单一本体态空间的经典本体论模型。我们证明了一个信息论不可行定理，表明此类模型必须承担不可约简的语境信息成本：语境依赖性无法完全通过本体态单独中介，而需要超越本体的额外语境信息。我们提供了一个构造性示例来说明这种阻碍，并证明其完全源于经典概率空间内本体态重复使用的要求。我们进一步阐释了量子理论如何通过放宽"所有测量统计皆源于单一底层经典本体变量"的假设来规避此阻碍。这些结果将语境性确立为对经典本体论模型的基本信息论约束，并阐明了其作为经典表示局限性的起源。