Hierarchies of multipartite entanglement for continuous-variable states

TL;DR

This paper introduces a hierarchy of criteria to analyze multipartite entanglement in continuous-variable quantum states, applicable to both Gaussian and non-Gaussian states, enhancing the understanding and detection of complex entanglement structures.

Contribution

It develops a unified hierarchy of separability criteria for multi-mode continuous-variable systems, applicable to broad classes of states, including Gaussian and non-Gaussian, with practical assessment methods.

Findings

Criteria effectively detect k-partite entanglement

Applicable to Gaussian and non-Gaussian states

Demonstrated with specific examples

Abstract

We derive a hierarchy of separability criteria for multi-mode continuous variable systems. They permit to study in a unified way the k-partite entanglement of broad classes of Gaussian and non- Gaussian states. With specific examples we demonstrate the strength of the criteria, and, we discuss their assessment based on data obtained from Gaussian measurements.