# Entanglement and squeezing in continuous-variable systems

## TL;DR

This paper introduces a new multi-mode squeezing coefficient for detecting entanglement in continuous-variable systems, applicable to Gaussian and non-Gaussian states, and capable of analyzing multipartite entanglement structures.

## Contribution

The paper presents a novel squeezing coefficient based on covariance matrices that efficiently characterizes and detects entanglement in multi-mode continuous-variable systems, including non-Gaussian states.

## Key findings

- The coefficient effectively detects entanglement in Gaussian states.
- Extensions allow for entanglement detection within specific system partitions.
- Application to nonlinear observables reveals non-Gaussian entanglement.

## Abstract

We introduce a multi-mode squeezing coefficient to characterize entanglement in $N$-partite continuous-variable systems. The coefficient relates to the squeezing of collective observables in the $2N$-dimensional phase space and can be readily extracted from the covariance matrix. Simple extensions further permit to reveal entanglement within specific partitions of a multipartite system. Applications with nonlinear observables allow for the detection of non-Gaussian entanglement.