Matched entanglement witness criteria for continuous variables

TL;DR

This paper develops new entanglement criteria for continuous variable quantum states using Gaussian operators, enabling precise detection of both Gaussian and non-Gaussian entanglement through covariance matrices.

Contribution

It introduces a novel approach transforming entanglement detection into a Bosonic Gaussian channel problem, providing necessary and sufficient criteria for a broad class of states.

Findings

Criteria applicable to Gaussian and non-Gaussian states

Explicit expression using covariance matrices

Enhanced detection of non-Gaussian entanglement

Abstract

We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. We transform the validity of a Gaussian witness to a Bosonic Gaussian channel problem. It follows that the maximal means of two-mode and some four-mode Gaussian operators over product pure states are achieved by vacuum (or coherent states and squeezed states) according to the properties of Bosonic Gaussian channels. Then we have necessary and sufficient criteria of separability not only for Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to or/and subtracting from Gaussian states. The criterion can be further explicitly expressed with covariance matrix of the Gaussian state or covariance matrix of Gaussian kernel of the non-Gaussian state. This opens a way for precise detection of non-Gaussian entanglement.