Realignment separability criterion assisted with filtration for detecting continuous-variable entanglement

TL;DR

This paper presents a new, physically implementable realignment criterion for detecting continuous-variable entanglement, enhanced by a filtration process that improves detection sensitivity, especially for Gaussian states.

Contribution

It introduces a weak realignment separability criterion suitable for continuous variables, and a filtration method that boosts entanglement detection, outperforming previous criteria in some cases.

Findings

Effective detection of continuous-variable entanglement.

Filtration enhances sensitivity beyond the original criterion.

Applicable to Gaussian states with improved performance.

Abstract

We introduce a weak form of the realignment separability criterion which is particularly suited to detect continuous-variable entanglement and is physically implementable (it requires linear optics transformations and homodyne detection). Moreover, we define a family of states, called Schmidt-symmetric states, for which the weak realignment criterion reduces to the original formulation of the realignment criterion, making it even more valuable as it is easily computable especially in higher dimensions. Then, we focus in particular on Gaussian states and introduce a filtration procedure based on noiseless amplification or attenuation, which enhances the entanglement detection sensitivity. In some specific examples, it does even better than the original realignment criterion.