A Symplectic Interpretation of the Separability of Gaussian Mixed States

TL;DR

This paper employs symplectic and Wigner formalism techniques to refine criteria for determining the separability of bipartite Gaussian mixed states across multiple dimensions.

Contribution

It introduces a symplectic approach to improve the Werner and Wolf separability criterion for Gaussian states, enabling characterization via comparison with pure Gaussian states.

Findings

Refined separability criterion for Gaussian states

Applicable to bipartite states in any dimension

Characterization of separability through comparison with pure states

Abstract

We prove, using symplectic methods and The Wigner formalism, a refinement of a criterion due to Werner and Wolf for the separability of bipartite Gaussian mixed states in an arbitrary number of dimensions. We use our result to show that one can characterize separability by comparing these states with separable pure Gaussian states.