Multipartite Gaussian Entanglement of Formation

TL;DR

This paper extends the Gaussian entanglement of formation to multipartite states, demonstrating its additivity and computability for three-mode Gaussian states, thus advancing understanding of complex quantum entanglement measures.

Contribution

It introduces a multipartite extension of Gaussian entanglement of formation and proves its additivity and computability for three-mode states.

Findings

The measure is fully additive for three-mode Gaussian states.

The measure is computable for three-mode Gaussian states.

Provides a new tool for quantifying multipartite Gaussian entanglement.

Abstract

Entanglement of formation is a fundamental measure that quantifies the entanglement of bipartite quantum states. This measure has recently been extended into multipartite states taking the name $\alpha$-entanglement of formation. In this work, we follow an analogous multipartite extension for the Gaussian version of entanglement of formation, and focusing on the the finest partition of a multipartite Gaussian state we show this measure is fully additive and computable for 3-mode Gaussian states.