On the disentanglement of Gaussian quantum states by symplectic rotations

Maurice A De Gosson

doi:10.5802/crmath.57

Abstract

We show that every Gaussian mixed quantum state can be disentangled by conjugation with a unitary operator corresponding to a symplectic rotation via the metaplectic representation of the symplectic group. The main tools we use are the Werner–Wolf condition for separability on covariance matrices and the symplectic covariance of Weyl pseudo-differential operators.

Highlights

Gaussian states play an ubiquitous role in quantum information theory and in quantum optics because they are easy to manufacture in the laboratory, and have in addition important extremality properties [12]
We show that every Gaussian mixed quantum state can be disentangled by conjugation with a unitary operator corresponding to a symplectic rotation via the metaplectic representation of the symplectic group
The aim of this Note is to show that every Gaussian state can be made separable by using a symplectic rotation and of the corresponding metaplectic operator

Summary

Introduction

Gaussian states play an ubiquitous role in quantum information theory and in quantum optics because they are easy to manufacture in the laboratory, and have in addition important extremality properties [12]. We show that every Gaussian mixed quantum state can be disentangled by conjugation with a unitary operator corresponding to a symplectic rotation via the metaplectic representation of the symplectic group. The main tools we use are the Werner–Wolf condition for separability on covariance matrices and the symplectic covariance of Weyl pseudo-differential operators.

Results

Conclusion