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.
@article{arxiv.2601.02350,
title = {Binarisation-loophole-free observation of high-dimensional quantum nonlocality},
author = {Jia-le Miao and Elna Svegborn and Zhuo Chen and Yu Guo and Xiao-Min Hu and Yun-Feng Huang and Chuan-Feng Li and Guang-Can Guo and Armin Tavakoli and Bi-Heng Liu},
journal= {arXiv preprint arXiv:2601.02350},
year = {2026}
}
Comments
6 pages, 4 figures. Supplemental material included