On synthesis of linear quantum stochastic systems by pure cascading

TL;DR

This paper characterizes which linear quantum stochastic systems can be realized solely through pure cascading of simpler systems, showing all passive systems can be realized this way, simplifying experimental implementation.

Contribution

It provides a precise characterization of passive linear quantum stochastic systems realizable by pure cascading without direct interaction Hamiltonians.

Findings

All passive linear quantum stochastic systems are realizable by pure cascading.

A constructive example demonstrates realization of a two degrees of freedom passive system.

The class of systems realizable by pure cascading is explicitly characterized.

Abstract

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 is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, realizations by pure cascading, without a direct interaction Hamiltonian, would be much simpler to implement and this raises the natural question of what class of linear quantum stochastic systems are realizable by cascading alone. This paper gives a precise characterization of this class of linear quantum stochastic systems and then it is proved that, in the weaker sense of transfer function realizability, all passive linear quantum stochastic systems belong to this class. A constructive example is given to show the transfer function realization of a two degrees of freedom passive linear quantum stochastic system by pure cascading.