Uniform Entanglement Frames

TL;DR

This paper develops universal criteria for detecting genuine multipartite entanglement using majorization theory and uncertainty relations, introducing geometric and witness-based methods for improved entanglement detection.

Contribution

It introduces a family of entanglement detectors based on majorization and uncertainty relations, along with geometric $k$-separable circles and a universal entanglement witness.

Findings

Family of entanglement detectors from uncertainty relations

Geometric $k$-separable circles for state classification

Universal entanglement witness for accurate detection

Abstract

We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of infinitely many detectors to check genuine multipartite entanglement. We also introduce the concept of $k$-separable circles via geometric distance for probability vectors, which include at most $(k-1)$-separable states. The entanglement witness is also generalized to a universal entanglement witness which is able to detect the $k$-separable states more accurately.