Global restrictions under local state discrimination

We investigate how local distinguishability can restrict global properties of bi-partite states. We begin exploring how non-locality becomes limited by optimal local state discrimination and observe a non-trivial trade-off between CHSH violation and success probability of local discrimination. We extend our findings to bounding the maximally entangled sate fidelity and global observables such as the energy. Our results show that optimal local state discrimination can become a powerful tool to limit global behaviours, e.g. from entangled adversaries in quantum cryptography.