Exact Quantum Maxima of the n-Cycle Overlap Inequalities

Summary. The paper shows that pairwise interference visibility measurements in multi-path interferometers provide an operational witness for preparation noncontextuality via overlap inequalities. Under ideal symmetric conditions, visibilities directly encode state overlaps without tomography or SWAP tests. For three paths, any jointly diagonalizable description satisfies V_{12}^2 + V_{23}^2 - V_{13}^2 ≤ 1, which pure qubit states violate up to a value of 5/4. This is generalized to n-path interferometers yielding the tight qubit bound S_n^max = n cos^2(π/2n) - 1 for n ≥ 3, achieved by coplanar pure states with uniform angular separation π/n. A robustness analysis supplies explicit experimental thresholds, and violations witness preparation contextuality under the operational equivalences of overlap-based generalized noncontextuality frameworks. For n-cycle inequalities, only the relevant pairwise visibilities need to be measured.

Significance. If the central derivations hold, this constitutes a useful operational advance by linking standard interferometric observables directly to preparation noncontextuality tests. The explicit qubit bounds, generalization to arbitrary n, and provision of robustness thresholds are strengths that facilitate experimental implementation in photonic systems. The manuscript supplies clean inequality derivations from overlap relations and falsifiable visibility predictions, which enhance its value for quantum foundations research.