In this paper, we study the Hardy nonlocal argument (HNA) and the Cabello nonlocal argument (CNA) under the Information Causality, Macroscopic Locality and Local Orthogonality principles in the context of Local Randomness. We see that, in the context of all the possibilities of local randomness, the gap between the quantum mechanics and the above principles, in the Cabello's nonlocality argument is larger than the Hardy's case. Therefore the CNA is stronger control than the HNA for detecting post-quantum nosignalling correlations.
Recent advancements have expanded Hardy's nonlocality arguments into multisetting and multidimensional systems to enhance quantum correlations. In comparison with Hardy's nonlocality argument, Cabello's nonlocality argument (CNA) emerges as a superior choice for illustrating nonlocal features. An open question persists regarding the potential extension of CNA to arbitrary (
k,d) scenarios. Here, we answer this question both in theory and experiment. Theoretically, by utilizing compatibility graphs, we construct a new logical framework for multisetting and multidimensional CNA, demonstrating an increase in the maximum successful probability with setting
k and dimension
d. Experimentally, by employing controllable photonic orbital angular momentum entanglement, we exhibit nonlocality with an experimentally recorded probability of 20.29% in the (2, 4) scenario and 28.72% in the (6, 2) scenario. Our work showcases a sharper contradiction between quantum mechanics and classical theory, surpassing the bound limited by the original version.