Binarisation-loophole-free observation of high-dimensional quantum nonlocality

TL;DR

This paper demonstrates a loophole-free test of high-dimensional quantum nonlocality using four-dimensional photonic entanglement and multi-outcome detection, confirming genuine high-dimensional quantum correlations.

Contribution

It introduces a method to close the binarisation loophole in high-dimensional Bell tests by employing multi-outcome measurements on four-dimensional entangled photons.

Findings

Observed violations of Bell inequalities confirming high-dimensional nonlocality.

Ruled out lower-dimensional quantum models, confirming genuine high-dimensional entanglement.

Demonstrated a loophole-free approach to high-dimensional quantum nonlocality tests.

Abstract

Bell inequality tests based on high-dimensional entanglement usually require measurements that can resolve multiple possible outcomes. However, the implementation of high-dimensional multi-outcome measurements is often only emulated via a collection of ``click or no-click'' measurements. This reduction of multi-outcome measurements to binary-outcome measurements opens a loophole in high-dimensional tests Bell inequalities which can be exploited by local hidden variable models [Tavakoli et al., Phys. Rev. A 111, 042433 (2025)]. Here, we close this loophole by using four-dimensional photonic path-mode entanglement and multi-outcome detection. We test both the well-known Collins-Gisin-Linden-Massar-Popescu inequality and a related Bell inequality tailored for maximally entangled states in high-dimension. We observe violations that are large enough to also rule out any quantum model based on entanglement of lower dimension, thereby demonstrating genuinely high-dimensional nonlocality free of the binarisation loophole.