Linear Quantum Feedback Networks

TL;DR

This paper develops a mathematical framework for linear quantum feedback networks, deriving transfer functions for various configurations and showing consistency with nonlinear cases, advancing the understanding of quantum control systems.

Contribution

It extends the theory of quantum feedback networks to linear Markovian systems, providing explicit transfer functions and algebraic rules for their analysis.

Findings

Transfer functions for linear quantum systems are derived.

The algebraic rules for nonlinear systems apply to linear cases.

Transfer functions for series, cascade, and feedback configurations are obtained.

Abstract

The mathematical theory of quantum feedback networks has recently been developed for general open quantum dynamical systems interacting with bosonic input fields. In this article we show, for the special case of linear dynamical systems Markovian systems with instantaneous feedback connections, that the transfer functions can be deduced and agree with the algebraic rules obtained in the nonlinear case. Using these rules, we derive the the transfer functions for linear quantum systems in series, in cascade, and in feedback arrangements mediated by beam splitter devices.