Global restrictions under local state discrimination

We investigate how local distinguishability can restrict global properties of states shared between two parties. We begin exploring how nonlocality becomes limited by local state discrimination and observe a nontrivial tradeoff between Clauser-Horne-Shimony-Holt (CHSH) violation and success probability of local discrimination. We extend our findings to bounding the maximally entangled state fidelity and global observables such as the energy. Our results show that local state discrimination can become a powerful tool to limit global behaviors, e.g., from entangled adversaries in quantum cryptography.