Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a fixed subsystem-level ontic state space is reused across multiple interventions. Our main result is an information-theoretic obstruction: whenever a classical single-state model reproduces operational statistics using an auxiliary contextual register, the required contextual information is lower-bounded by the conditional mutual information $I(C;O\mid λ)$ between intervention $C$ and outcome $O$ conditioned on the subsystem ontic state $λ$. The mathematical inequality itself is elementary, but its interpretive significance is structural: under shared-state reuse, contextual distinctions need not be fully internalized within the subsystem ontic state alone. We provide a constructive illustration of this point and clarify how the issue should be understood as a limitation of subsystem-level classical representation, rather than as a dualism about physical reality. We further discuss how this perspective relates to ontological models and to contextuality in quantum foundations.

翻译：语境性是量子理论的核心特征，传统上被理解为使用非语境本体模型无法再现量子测量统计。我们研究了经典本体描述，其中固定的子系统级本体态空间在多次干预中被重复使用。我们的主要结果是一种信息论障碍：每当经典单态模型通过辅助语境寄存器再现操作统计时，所需的语境信息下界由条件互信息 $I(C;O\mid λ)$ 给出，其中 $C$ 是干预，$O$ 是结果，$\lambda$ 是子系统本体态。该数学不等式本身是基本的，但其解释意义是结构性的：在共享态重复使用下，语境区分不必完全内化于子系统本体态中。我们对此进行了建设性说明，并阐明了该问题应被理解为子系统级经典表示的局限性，而非对物理实在的二元论。我们进一步讨论了这一观点与本体模型及量子基础中语境性的关联。