Characterizing Nonlocal Correlations via Universal Uncertainty Relations

Characterization and certification of nonlocal correlations is one of the the central topics in quantum information theory. In this work, we develop the detection methods of entanglement and steering based on the universal uncertainty relations and fine-grained uncertainty relations. In the course of our study, the uncertainty relations are formulated in majorization form, and the uncertainty quantifier can be chosen as any convex Schur concave functions, this leads to a large set of inequalities, including all existing criteria based on entropies. We address the question that if all steerable states (or entangled states) can be witnessed by some uncertainty-based inequality, we find that for pure states and many important families of states, this is the case.