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

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The mathematical theory of quantum feedback networks has recently been developed by Gough and James 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 ⋆-unitary version of the Siegel identities.