Hierarchy of Separability Conditions for Bipartite Systems

TL;DR

This paper introduces a new hierarchy of necessary separability conditions for bipartite quantum states, using higher powers of density operators, which helps identify entanglement.

Contribution

It develops a novel hierarchy of separability criteria based on higher powers of density operators, extending previous methods.

Findings

Hierarchy provides necessary conditions for separability.

Violation indicates entanglement.

Eigenvalue-based condition derived from hierarchy.

Abstract

A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite system and the reduced density operators of the subsystems. Violation of any of the conditions in the hierarchy implies entanglement. As a consequence of the hierarchy, another separability condition, expressed in terms of the eigenvalues of the density operators of the total system and subsystems, is obtained.