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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…

This paper provides an alternative approach to the problem of preparing pure Gaussian states in a linear quantum system. It is shown that any pure Gaussian state can be generated by a cascade of one-dimensional open quantum harmonic…

Recently, it has been demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simpler one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which…

This paper establishes that generic linear quantum stochastic systems have a pure cascade realization of their transfer function, generalizing an earlier result established only for the special class of completely passive linear quantum…

Recently the complete characterization of a general Gaussian dissipative system having a unique pure steady state was obtained in [Koga and Yamamoto 2012, Phys. Rev. A 85, 022103]. This result provides a clear guideline for engineering an…

This paper is concerned with the generation of Gaussian invariant states in cascades of open quantum harmonic oscillators governed by linear quantum stochastic differential equations. We carry out infinitesimal perturbation analysis of the…

Fluctuation dissipation theorems connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many…

The purpose of this paper is to study the realization theory of quantum linear systems. It is shown that for a general quantum linear system its controllability and observability are equivalent and they can be checked by means of a simple…

We investigate the problem of preparing a pure Gaussian state via reservoir engineering. In particular, we consider a linear quantum system with a passive Hamiltonian and with a single reservoir which acts only on a single site of the…

The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…

Quantum cascaded systems offer the possibility to manipulate a target system with the quantum state of a source system. Here, we study in detail the differences between a direct quantum cascade and coherent/incoherent driving for the case…

Gaussian bipartite states are basic tools for the realization of quantum information protocols with continuous variables. Their complete characterization is obtained by the reconstruction of the corresponding covariance matrix. Here we…

The realization of transfer functions of Linear Quantum Stochastic Systems (LQSSs) is an issue of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. In this…

This paper provides some necessary and sufficient conditions for a generalMarkovian Gaussian master equation to have a unique pure steady state. The conditions are described by simple matrix equations; thus the so-called environment…

This paper aims to provide conditions under which a quantum stochastic differential equation can serve as a model for interconnection of a bilinear system evolving on an operator group SU(2) and a linear quantum system representing a…

We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of $(2\aleph+1)$ quantum harmonic oscillators where the central oscillator of the chain is coupled to a…

We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a…

We compute the quantum maximal correlation for bipartite Gaussian states of continuous-variable systems. Quantum maximal correlation is a measure of correlation with the monotonicity and tensorization properties that can be used to study…

We consider the transfer functions describing the input-output relation for a class of linear open quantum systems involving feedback with nonzero time delays. We show how such transfer functions can be factorized into a product of terms…

It is often convenient to separate a state estimation task into smaller "local" tasks, where each local estimator estimates a subset of the overall system state. However, neglecting cross-covariance terms between state estimates can result…