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

Quantum contextuality can be interpreted as an information-capacity signature of a structural limitation on physical distinguishability. This paper develops that claim from 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. On this basis, the paper introduces a capacity measure of effective distinguishability: for finite families of pure states within a single measurement context, the measure is given by the dimension of their linear span, while for mixed states it is defined as the exponential of the von Neumann entropy. 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 way, contextuality is reconstructed as a structural consequence of constrained distinguishability rather than treated as an isolated axiom. The paper also relates this framework to topological quantization phenomena and to contemporary discussions in quantum foundations and quantum information.