Photonic families of non-Gaussian entangled states and entanglement criteria for continuous-variable systems

TL;DR

This paper introduces non-Gaussian entangled states generated from number states and explores entanglement criteria beyond second moments, revealing limitations of Gaussian-based measures for certain non-Gaussian states.

Contribution

It presents new classes of non-Gaussian entangled states and develops higher-order moment criteria to detect their entanglement, surpassing Gaussian covariance matrix methods.

Findings

Covariance matrix criteria fail for many non-Gaussian states.

Higher-order moment criteria can verify entanglement in these states.

Some non-Gaussian states appear separable under Gaussian measures.

Abstract

We consider two classes of non-Gaussian entangled states generated from the product of number states with the action of the beamsplitter or the two-mode squeezer. It is shown that, for many of these states, the covariance matrix is compatible with the covariance matrix of separable Gaussian states and their separability cannot be verified by the measurements of the first and second moments of canonical variables. We identify a couple of continuous-variable entanglement criteria with higher order moments to verify these non-Gaussian entanglement.