Entanglement Detection via Direct-Sum Majorization Uncertainty Relations

TL;DR

This paper develops entanglement detection methods using direct-sum majorization uncertainty relations, providing necessary conditions that improve with the system's dimension, applicable to multiple observables.

Contribution

It introduces novel entanglement detection techniques based on direct-sum majorization uncertainty relations for multiple observables.

Findings

Detection methods are nonlinear and effective for high-dimensional systems.

Number of entanglement criteria increases with system dimension.

Applicable to both two and many observables.

Abstract

In this paper we investigate the relationship between direct-sum majorization formulation of uncertainty relations and entanglement, for the case of two and many observables. Our primary results are entanglement detection methods based on direct-sum majorization uncertainty relations. These nonlinear detectors provide a set of necessary conditions for detecting entanglement whose number grows with the dimension of the state being detected.