The action cost of information: A structural framework for quantum contextuality

Quantum contextuality can be viewed as an information-capacity signature of a structural limitation on physical distinguishability. We adopt, as a working principle, a coherence threshold formulated in terms of prequantum holonomy: physically distinguishable alternatives are associated with admissible phase-space loops whose accumulated action cannot be made arbitrarily small, with the scale set by the reduced Planck constant.To translate this principle into a quantitative state-space constraint, we introduce a capacity measure of effective distinguishability. For finite families of pure states within a single measurement context, the capacity is the dimension of their linear span; for mixed states, it is given by the exponential of the von Neumann entropy (in nats). The measure is additive within a commuting context, but becomes subadditive across incompatible contexts, with strict subadditivity whenever the corresponding Hilbert subspaces overlap. In this sense, contextuality is captured here as a subadditivity-based witness of constrained distinguishability implied by the action budget.The framework connects the holonomy-based coherence threshold to non-additive effective state counting and relates this viewpoint to topological quantization phenomena, including flux quantization and protected modes, by interpreting them as manifestations of globally consistent phase structure under action quantization.