Purification of Gaussian maximally mixed states

TL;DR

This paper explores the purification of Gaussian maximally mixed states, demonstrating that their purifications are Gaussian maximally entangled states, and develops a formalism for Gaussian purification in continuous-variable quantum systems.

Contribution

It introduces a formal framework for Gaussian purification of GMMSs and constructs new Gaussian maximally entangled states in the continuous-variable regime.

Findings

Purifications of GMMSs are Gaussian maximally entangled states.

A general formalism for Gaussian purification process is developed.

Purified states exhibit maximal Gaussian entanglement.

Abstract

We find that the purifications of several Gaussian maximally mixed states (GMMSs) correspond to some Gaussian maximally entangled states (GMESs) in the continuous-variable regime. Here, we consider a two-mode squeezed vacuum (TMSV) state as a purification of the thermal state and construct a general formalism of the Gaussian purification process. Moreover, we introduce other kind of GMESs via the process. All of our purified states of the GMMSs exhibit Gaussian profiles; thus, the states show maximal quantum entanglement in the Gaussian regime.