Gaussian entanglement of symmetric two-mode Gaussian states

TL;DR

This paper introduces a measure of entanglement for symmetric two-mode Gaussian states based on their distance to separable states, and finds that Bures-distance aligns with the entanglement of formation.

Contribution

It defines a Gaussian entanglement measure using Bures distance and relative entropy, and demonstrates Bures-distance's consistency with entanglement of formation.

Findings

Bures-distance Gaussian entanglement matches the entanglement of formation.

Diagonalization of covariance matrices simplifies entanglement calculations.

Uhlmann fidelity's multiplicativity aids in the analysis.

Abstract

A Gaussian degree of entanglement for a symmetric two-mode Gaussian state can be defined as its distance to the set of all separable two-mode Gaussian states. The principal property that enables us to evaluate both Bures distance and relative entropy between symmetric two-mode Gaussian states is the diagonalization of their covariance matrices under the same beam-splitter transformation. The multiplicativity property of the Uhlmann fidelity and the additivity of the relative entropy allow one to finally deal with a single-mode optimization problem in both cases. We find that only the Bures-distance Gaussian entanglement is consistent with the exact entanglement of formation.