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, Snmax=ncos2(π/(2n))−1, for arbitrary cycle length n≥3. 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→∞, with corresponding visibility thresholds. Within generalized noncontextuality frameworks, and subject to the required operational equivalences, such violations can witness preparation contextuality.
Versions
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BibTeX
@misc{siddiqui2026exact,
title = {{Exact Quantum Maxima of the $n$-Cycle Overlap Inequalities}},
author = {Mohd Asad Siddiqui},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.14395},
eprint = {2605.14395},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.14395},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Quantum Maxima of the n-Cycle Overlap Inequalities
AU - Mohd Asad Siddiqui
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2605.14395
UR - https://arxiv.org/abs/2605.14395
AB - 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=ncos^2(π/(2n))−1, for arbitrary cycle length n≥3. 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→∞, with corresponding visibility thresholds. Within generalized noncontextuality frameworks, and subject to the required operational equivalences, such violations can witness preparation contextuality.
ER -