# Quantifying entanglement in two-mode Gaussian states

## TL;DR

This paper derives an analytical lower bound for the entanglement of formation in two-mode Gaussian states, improving quantification accuracy over the commonly used logarithmic negativity, especially for symmetric and balanced states.

## Contribution

It introduces a new analytical lower bound for entanglement of formation in two-mode Gaussian states, addressing limitations of existing measures.

## Key findings

- Lower bound is tight for symmetric states
- Provides simple expressions for relevant physical cases
- Highlights issues with logarithmic negativity as a measure

## Abstract

Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.