Interference visibility as a witness of preparation contextuality via overlap inequalities

TL;DR

This paper demonstrates that multi-path interferometry can operationally test preparation noncontextuality through visibility measurements, deriving bounds that are violated by quantum states, thus witnessing contextuality.

Contribution

It introduces a method linking interference visibility to preparation contextuality, deriving new bounds for multi-path interferometers and experimental thresholds for violations.

Findings

Derived bounds for visibility in multi-path interferometers under noncontextual models.

Quantum states can violate these bounds, witnessing contextuality.

Provided explicit experimental thresholds for observing violations.

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.