# Characterizing Nonlocal Correlations via Universal Uncertainty Relations

## TL;DR

This paper introduces new methods for detecting quantum entanglement and steering using universal and fine-grained uncertainty relations formulated through majorization, covering a broad set of existing criteria.

## Contribution

It develops a unified framework for entanglement and steering detection based on majorization-form uncertainty relations, encompassing all entropy-based criteria.

## Key findings

- Universal uncertainty relations can witness all pure steerable and many entangled states.
- The framework generalizes existing entropy-based criteria.
- It provides a large set of inequalities for quantum correlation detection.

## Abstract

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.