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arxiv: 2605.14395 · v2 · pith:A62LWZBBnew · submitted 2026-05-14 · 🪐 quant-ph

Interference visibility as a witness of preparation contextuality via overlap inequalities

Mohd Asad Siddiqui This is my paper

Pith reviewed 2026-05-19 16:39 UTC · model grok-4.3

classification 🪐 quant-ph
keywords preparation contextualityinterference visibilitymulti-path interferometryoverlap inequalitiesquantum noncontextualityqubit statesgeneralized noncontextuality
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The pith

Pairwise visibility measurements in multi-path interferometers witness preparation contextuality via violated overlap inequalities.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows 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 description must satisfy V12 squared plus V23 squared minus V13 squared at most 1, but pure qubit states violate this bound and reach a value of 5/4. The result generalizes to arbitrary n-path interferometers with the tight qubit bound of n times cosine squared of pi over 2n minus 1, achieved by coplanar pure qubit states with uniform angular separation.

Core claim

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 V12² + V23² - V13² ≤ 1, where Vij are two-path visibilities. Pure qubit detector states violate this bound, achieving a maximal value of 5/4. The generalization yields the tight qubit bound Sn^max = n cos²(π/2n) - 1 for all n ≥ 3, achieved by coplanar pure qubit states with uniform angular separation π/n. Under the operational equivalences used in overlap-based generalized noncontextuality frameworks, violations of these visibility inequalities witness preparation contextual

What carries the argument

Visibility inequalities derived from pairwise measurements that bound possible state overlaps in jointly diagonalizable descriptions of n-path interferometers.

Load-bearing premise

The system operates under ideal symmetric conditions with jointly diagonalizable coherence-free descriptions that respect the operational equivalences of overlap-based noncontextuality frameworks.

What would settle it

Measure the three pairwise visibilities in a symmetric three-path interferometer prepared with a pure qubit state and check whether their squares satisfy V12² + V23² - V13² > 1.

Figures

Figures reproduced from arXiv: 2605.14395 by Mohd Asad Siddiqui.

Figure 1
Figure 1. Figure 1: FIG. 1. Optimal Bloch-vector configurations for the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
read the original 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 $S_n^{\max}=n\cos^2(\pi/2n)-1$ for all $n\ge3$, achieved by coplanar pure qubit states with uniform angular separation $\pi/n$. 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

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.

minor comments (3)
  1. In the section deriving the three-path inequality, explicitly number and reference the key overlap-to-visibility mapping equations to improve traceability of the steps from operational equivalences to the bound V_{12}^2 + V_{23}^2 - V_{13}^2 ≤ 1.
  2. The robustness analysis should include a brief table or plot summarizing the experimental visibility thresholds as a function of noise parameters for quick reference by experimental groups.
  3. Clarify the notation for S_n^max in the generalization section by providing its explicit definition immediately before the bound is stated, rather than relying primarily on the abstract.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary and recommendation of minor revision. The assessment correctly captures the main results on visibility inequalities as witnesses of preparation contextuality.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper maps pairwise visibilities to state overlaps under explicit ideal symmetric conditions, derives the inequality V12² + V23² - V13² ≤ 1 for jointly diagonalizable descriptions directly from those overlap relations, exhibits explicit violation by pure qubit states, and obtains the general bound Sn^max = n cos²(π/2n) - 1 via standard trigonometric maximization over coplanar states. These steps are algebraic and geometric calculations independent of the target contextuality conclusion. The final link to preparation noncontextuality is stated as following from pre-existing operational equivalences in overlap-based generalized noncontextuality frameworks rather than being presupposed or fitted within the present derivation. No self-citation chain, ansatz smuggling, or reduction of a claimed prediction to a fitted input is present in the provided derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the noncontextuality assumption for jointly diagonalizable descriptions and the operational equivalences of overlap-based generalized noncontextuality frameworks; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Jointly diagonalizable (coherence-free) descriptions must satisfy the visibility inequality under ideal symmetric conditions.
    Invoked to derive the bound V12² + V23² - V13² ≤ 1 for three paths and its generalization.
  • domain assumption Operational equivalences in overlap-based generalized noncontextuality frameworks allow visibility violations to witness preparation contextuality.
    Stated as the link between the inequalities and contextuality for n-cycle cases.

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