Cascade and locally dissipative realizations of linear quantum systems for pure Gaussian state covariance assignment

TL;DR

This paper introduces two methods for constructing linear quantum systems that generate specific pure Gaussian states, one using cascade connections and the other employing local dissipation, with practical examples in quantum optics.

Contribution

It proposes novel cascade and locally dissipative realizations for pure Gaussian state covariance assignment in linear quantum systems.

Findings

Both realizations can generate any pure Gaussian state under certain conditions.

Examples demonstrate the practical implementation in quantum optics.

The locally dissipative method requires specific covariance matrix conditions.

Abstract

This paper presents two realizations of linear quantum systems for covariance assignment corresponding to pure Gaussian states. The first one is called a cascade realization; given any covariance matrix corresponding to a pure Gaussian state, we can construct a cascaded quantum system generating that state. The second one is called a locally dissipative realization; given a covariance matrix corresponding to a pure Gaussian state, if it satisfies certain conditions, we can construct a linear quantum system that has only local interactions with its environment and achieves the assigned covariance matrix. Both realizations are illustrated by examples from quantum optics.