Linear quantum systems with diagonal passive Hamiltonian and a single dissipative channel

TL;DR

This paper characterizes a simple class of linear quantum systems with diagonal passive Hamiltonians and one dissipative channel capable of generating specific pure Gaussian states, simplifying practical implementation.

Contribution

It provides a parametrization of pure Gaussian state covariance matrices achievable by these specialized linear quantum systems.

Findings

Identifies a class of pure Gaussian states realizable with simple quantum systems.

Provides a parametrization linking covariance matrices to system parameters.

Simplifies the design of practical quantum systems for state preparation.

Abstract

Given any covariance matrix corresponding to a so-called pure Gaussian state, a linear quantum system can be designed to achieve the assigned covariance matrix. In most cases, however, one might obtain a system that is difficult to realize in practice. In this paper, we restrict our attention to a special class of linear quantum systems, i.e., systems with diagonal passive Hamiltonian and a single dissipative channel. The practical implementation of such a system would be relatively simple. We then parametrize the class of pure Gaussian state covariance matrices that can be achieved by this particular type of linear quantum system.