The Gough-James Theory of Quantum Feedback Networks in the Belavkin Representation

TL;DR

This paper reformulates the Gough-James quantum feedback network theory using Belavkin matrices, revealing a non-commutative Mobius transformation and establishing a $\

Contribution

It introduces a Belavkin matrix-based formulation of quantum feedback networks, connecting feedback reduction to non-commutative Mobius transformations and $\

Findings

Feedback reduction formula expressed via Belavkin matrices

Identification of a non-commutative Mobius transformation

Establishment of a $\

Abstract

The mathematical theory of quantum feedback networks has recently been developed by Gough and James \cite{QFN1} for general open quantum dynamical systems interacting with bosonic input fields. In this article we show, that their feedback reduction formula for the coefficients of the closed-loop quantum stochastic differential equation can be formulated in terms of Belavkin matrices. We show that the reduction formula leads to a non-commutative Mobius transformation based on Belavkin matrices, and establish a $\star$-unitary version of the Siegel identities.