Entanglement Detection Using Majorization Uncertainty Bounds

TL;DR

This paper introduces new entanglement detection criteria based on majorization uncertainty bounds, providing both linear and nonlinear tests that can identify entanglement in bipartite quantum states.

Contribution

It develops the first majorization-based entanglement criteria, including scalar measures, advancing the theoretical tools for quantum entanglement detection.

Findings

Criteria successfully detect entanglement in Werner states

Majorization relations effectively compare quantum disorder

Infinite scalar criteria derived from quasi-entropic measures

Abstract

Entanglement detection criteria are developed within the framework of the majorization formulation of uncertainty. The primary results are two theorems asserting linear and nonlinear separability criteria based on majorization relations, the violation of which would imply entanglement. Corollaries to these theorems yield infinite sets of scalar entanglement detection criteria based on quasi-entropic measures of disorder. Examples are analyzed to probe the efficacy of the derived criteria in detecting the entanglement of bipartite Werner states. Characteristics of the majorization relation as a comparator of disorder uniquely suited to information-theoretical applications are emphasized throughout.