Binarization-Loophole-Free Observation of High-Dimensional Quantum Nonlocality

Bell inequality tests based on high-dimensional entanglement usually require measurements that can resolve multiple possible outcomes. However, the implementation of high-dimensional multioutcome measurements is often only emulated via a collection of "click or no-click" measurements. This reduction of multioutcome measurements to binary-outcome measurements opens a loophole in high-dimensional tests Bell inequalities that can be exploited by local hidden variable models [Tavakoli et al., Phys. Rev. A 111, 042433 (2025)PLRAAN2469-992610.1103/PhysRevA.111.042433]. Here, we close this loophole by using four-dimensional photonic path-mode entanglement and multioutcome 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 binarization loophole.