Gaussian entanglement witness and refined Werner-Wolf criterion for continuous variables

TL;DR

This paper introduces a novel Gaussian entanglement witness and refines the Werner-Wolf criterion, providing a more comprehensive separability test for continuous variable quantum states, including non-Gaussian and two-mode states.

Contribution

It develops a matched quantum entanglement witness based on Gaussian operators, transforming the problem into an eigenvalue problem, and refines the Werner-Wolf criterion for better separability detection.

Findings

The witness is effective for symmetric and non-Gaussian states.

A necessary and sufficient criterion is established for two-mode squeezed thermal states.

The refined Werner-Wolf criterion improves separability detection accuracy.

Abstract

We use matched quantum entanglement witnesses to study the separable criteria of continuous variable states. The witness can be written as an identity operator minus a Gaussian operator. The optimization of the witness then is transformed to an eigenvalue problem of a Gaussian kernel integral equation. It follows a separable criterion not only for symmetric Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to or/and subtracting from symmetric Gaussian states. Based on Fock space numeric calculation, we obtain an entanglement witness for more general two-mode states. A necessary criterion of separability follows for two-mode states and it is shown to be necessary and sufficient for a two mode squeezed thermal state and the related two-mode non-Gaussian states. We also connect the witness based criterion with Werner-Wolf criterion and refine the Werner-Wolf criterion.