Detection of non-Gaussian entangled states with an improved continuous-variable separability criterion

TL;DR

This paper presents an enhanced separability criterion for continuous-variable quantum states that detects non-Gaussian entanglement more effectively by incorporating the degree of Gaussianity, surpassing traditional covariance matrix-based methods.

Contribution

The authors introduce a novel entanglement detection criterion that leverages Gaussianity measures to identify non-Gaussian entangled states missed by previous criteria.

Findings

Detects non-Gaussian entangled states undetected by Duan-Simon criterion

Uses Gaussianity degree to strengthen entanglement detection

Demonstrates families of states with improved detection capability

Abstract

Currently available separability criteria for continuous-variable states are generally based on the covariance matrix of quadrature operators. The well-known separability criterion of Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] , for example, gives a necessary and sufficient condition for a two-mode Gaussian state to be separable, but leaves many entangled non-Gaussian states undetected. Here, we introduce an improvement of this criterion that enables a stronger entanglement detection. The improved condition is based on the knowledge of an additional parameter, namely the degree of Gaussianity, and exploits a connection with Gaussianity-bounded uncertainty relations [Phys. Rev. A 86, 030102 (2012)]. We exhibit families of non-Gaussian entangled states whose entanglement remains undetected by the Duan-Simon criterion.