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arXiv:2605.14395

Interference visibility as a witness of preparation contextuality via overlap inequalities

Mohd Asad Siddiqui

quant-phSubmitted May 14, 2026• Announced May 15, 2026• 0 citations• Revised May 15, 2026 (v2)
v1 · May 14, 2026v2 · May 15, 2026v3 · Jun 9, 2026v4 · Sep 30, 2026
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Abstract

We show that standard multi-path interferometry, using only pairwise visibility measurements, provides an operational route to tests of preparation noncontextuality. Under ideal symmetric conditions, interference visibility directly encodes state overlaps, without requiring tomography or SWAP tests. For three paths, any jointly diagonalizable (coherence-free) description must satisfy $V_{12}^2+V_{23}^2-V_{13}^2\le 1$, where $V_{ij}$ are two-path visibilities. Pure qubit detector states violate this bound, achieving a maximal value of $5/4$. We generalize to arbitrary $n$-path interferometers and derive the tight qubit bound $S_n^{\max}=n\cos^2(π/2n)-1$ for all $n\ge3$, achieved by coplanar pure qubit states with uniform angular separation $π/n$. A robustness analysis yields explicit experimental thresholds. Under the operational equivalences used in overlap-based generalized noncontextuality frameworks, violations of these visibility inequalities also witness preparation contextuality. For $n$-cycle inequalities, only the pairwise visibilities appearing in the cycle need to be measured.

DOI
10.1098/rspa.2026.0596
Comments
9 pages, 1 figure, minor revisions with corrected visibility thresholds

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This preprint introduces a dynamical qutrit coherence-cycle witness based on calibrated pairwise visibility measurements in a three-path interferometer. The central idea is that pairwise visibility data contain a geometry of normalized qutrit coherences that is not captured by scalar coherence measures alone. For nonzero path populations, the population-calibrated two-path visibility equals the normalized off-diagonal coherence of the reduced path qutrit. The squared normalized coherences define the cycle expression Scyc = kappa_12^2 + kappa_23^2 - kappa_13^2. Classical jointly diagonalizable overlap geometries obey the boundary Scyc <= 1. A statistically certified value Scyc > 1 therefore indicates a nonclassical cyclic arrangement of pair coherences, rather than merely a large amount of coherence. The paper proves the physical qutrit range Scyc <= 5/4, gives explicit positive semidefinite qutrit examples with equal scalar coherence but different cycle geometry, constructs a completely positive random-unitary dephasing model with time-dependent geometry windows, and formulates a finite-data certification protocol including calibration and covariance propagation. The static overlap-cycle inequality is imported from prior overlap-cycle work; the new contribution is its calibrated realization as a path-qutrit coherence-geometry witness. The proposed witness is intended as a measurement-efficient diagnostic of normalized coherence geometry in multipath interferometry and open qutrit dynamics. It is not a full state-tomography method and does not by itself constitute a complete contextuality experiment; stronger interpretations require the additional operational assumptions stated in the manuscript.
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The problem of separating classical from quantum correlations is, in general, intractable and has been solved explicitly only in a few cases. In particular, known methods cannot provide general solutions for an arbitrary number of settings. We provide the complete characterization of the classical correlations and the corresponding maximal quantum violations for the case of $n\ensuremath{\ge}4$ observables ${X}_{0},...,{X}_{n\ensuremath{-}1}$, where each consecutive pair Xi,Xi+1{{X}_{i},{X}_{i+1}}Xi​,Xi+1​, sum modn\mathrm{mod}\phantom{\rule{0.16em}{0ex}}nmodn, is jointly measurable. This generalizes both the Clauser-Horne-Shimony-Holt and the Klyachko-Can-Binicio\ifmmode \breve{g}\else \u{g}\fi{}lu-Shumovsky scenarios, which are the simplest ones for locality and noncontextuality, respectively. In addition, we provide explicit quantum states and settings with maximal quantum violation and minimal quantum dimension.
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