Scaling Separability Criterion: Application To Gaussian States

TL;DR

This paper presents a modified separability criterion for Gaussian states that overcomes limitations of previous criteria, providing a more general and consistent method for detecting entanglement in multi-mode Gaussian states.

Contribution

The authors introduce a new, more general separability criterion that effectively detects entanglement in Gaussian states where previous criteria fail.

Findings

New criterion detects entanglement missed by earlier methods

Reproduces main features of scaling criteria across different states

Demonstrates higher generality and reliability of the modified criterion

Abstract

We introduce examples of three- and four-mode entangled Gaussian mixed states that are not detected by the scaling and Peres-Horodecki separability criteria. The presented modification of the scaling criterion resolves this problem. Also it is shown that the new criterion reproduces the main features of the scaling pictures for different cases of entangled states, while the previous versions lead to completely different outcomes. This property of the presented scheme is evidence of its higher generality.