Orbital angular momentum entanglement experiment bounding the predictive power of physical theories.

Whether quantum mechanics is predictively complete remains a fundamental question in its foundations. While most investigations have concentrated on two-dimensional systems, high-dimensional systems are more general and hold broader applicability. Extending the non-extensibility theorem by Colbeck and Renner [Nat. Commun.2, 411 (2011)10.1038/ncomms1416], we demonstrate that no alternative theory can enhance the predictive power of quantum mechanics in arbitrary dimensions. By linking the maximal predictive power achievable to experimentally observable correlations, we establish optimal experimental bounds exploiting orbital angular momentum entangled photon pairs. These results impose strict constraints and rule out a broad class of hidden-variable models, including Bell-type and Leggett-type theories, thereby reinforcing the completeness of quantum theory and advancing high-dimensional quantum cryptography.