Exact Quantum Maxima of the $n$-Cycle Overlap Inequalities

Abstract:We extend the three-state overlap analysis to determine the exact quantum maximum over finite-dimensional pure-state realizations of the $n$-cycle overlap inequalities, $S_n^{\max}=n\cos^2(\pi/(2n))-1$, for arbitrary cycle length $n\ge3$. The bound is saturated by an explicit family of coplanar qubit states equally spaced along a Fubini--Study geodesic, establishing dimensional saturation of the overlap-cycle hierarchy. Thus, the global optimum over all finite-dimensional pure-state realizations is already achieved in dimension two. We further show how, under ideal symmetric interferometric conditions, the overlap quantities can be inferred from pairwise fringe visibilities. The three-state case recovers the known maximum $5/4$, while the exact $n$-cycle result shows that the quantum--classical gap approaches one as $n\to\infty$, with corresponding visibility thresholds. Within generalized noncontextuality frameworks, and subject to the required operational equivalences, such violations can witness preparation contextuality.

arXiv:2605.14395 [quant-ph]

(or arXiv:2605.14395v4 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.14395 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1098/rspa.2026.0596 Focus to learn more DOI(s) linking to related resources

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