Tailored two-photon correlation and fair-sampling: a cautionary tale

TL;DR

This paper reports an experimental test of Bell inequality violations using orbital angular momentum states, revealing that fair-sampling assumptions can lead to apparent super-quantum correlations in high-dimensional quantum systems.

Contribution

The study demonstrates how specific measurement designs can produce apparent violations beyond quantum limits, emphasizing the importance of fair-sampling assumptions in high-dimensional Bell tests.

Findings

Achieved Bell parameter S=3.99, exceeding Tsirelson bound

Identified subtle fair-sampling violations affecting Bell test results

Highlighted risks of misinterpreting correlations in high-dimensional quantum experiments

Abstract

We demonstrate an experimental test of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality which seemingly exhibits correlations beyond the limits imposed by quantum mechanics. Inspired by the idea of Fourier synthesis, we design analysers that measure specific superpositions of orbital angular momentum (OAM) states, such that when one analyser is rotated with respect to the other, the resulting coincidence curves are similar to a square-wave. Calculating the CHSH Bell parameter, $S$, from these curves result to values beyond the Tsirelson bound of $S_{QM}=2\sqrt{2}$. We obtain $S=3.99\pm0.02$, implying almost perfect nonlocal Popescu-Rohrlich correlations. The "super-quantum" values of $S$ is only possible in our experiment because our experiment, subtly, does not comply with fair-sampling. The way our Bell test fails fair-sampling is not immediately obvious and requires knowledge of the states being measured. Our experiment highlights the caution needed in Bell-type experiments based on measurements within high-dimensional state spaces such as that of OAM, especially in the advent of device-independent quantum protocols.