A unifying separability criterion based on extended correlation tensor

TL;DR

This paper introduces a new, unified separability criterion based on the correlation tensor, which simplifies entanglement detection and unifies previous criteria, with practical applications demonstrated through examples.

Contribution

It proposes a novel, unified separability criterion using matrix decomposition that is stronger and more practical than existing methods.

Findings

Unifies multiple existing separability criteria.

Demonstrates effectiveness through theoretical analysis and examples.

Constructs a family of entanglement witnesses based on the criterion.

Abstract

Entanglement is fundamental inasmuch because it rephrases the quest for the classical-quantum demarcation line, and it also has potentially enormous practical applications in modern information technology. In this work, employing the approach of matrix decomposition, we introduce and formulate a practicable criterion for separability based on the correlation tensor. It is interesting that this criterion unifies several relevant separability criteria proposed before, even stronger than some of them. Theoretical analysis and detailed examples demonstrate its availability and feasibility for entanglement detection. Furthermore we build a family of entanglement witnesses using the criterion according to its linearity in the density operator space.