  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.
