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

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

2010-05-31

arxiv.org/abs/1005.5644v1

Physics

Mathematical Physics

8 pages, no figures To be submited Russian Journal of Mathematical Physics

Scientific paper

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.

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