Entanglement of formation for an arbitrary two-mode Gaussian state

TL;DR

This paper derives an exact method to compute the entanglement of formation for any two-mode Gaussian state, demonstrating its equivalence to the Gaussian entanglement measure and proving its additivity.

Contribution

It provides a closed-form solution for the entanglement of formation of two-mode Gaussian states and confirms its additivity, advancing quantum information theory.

Findings

Entanglement of formation equals the Gaussian entanglement measure.

Optimal pure-state decomposition for two-mode Gaussian states is derived.

Additivity of the entanglement of formation is proven.

Abstract

We write the optimal pure-state decomposition of any two-mode Gaussian state and show that its entanglement of formation coincides with the Gaussian one. This enables us to develop an insightful approach of evaluating the exact entanglement of formation. Its additivity is finally proven.