Hierarchies of entanglement potentials reveal intrinsic quantum state nonclassicality

Entanglement potentials are a promising method for the characterization of quantum state nonclassicality. Although they possess several interesting benefits, they critically rely on a well-tailored interaction between the tested state and a suitable classical state. We analyze the effect of imperfections in the interaction that are in real experiments to some extent always unavoidable. Furthermore, we study hierarchies of several entanglement potentials allowing us to detect these imperfections and, thus, preventing from misjudging the true intrinsic nonclassicality of the investigated states. The proposed idea is demonstrated in a proof-of-principle experiment on the platform of linear optics.