  Quantum feedback networks have been introduced in quantum optics as a set of
rules for constructing arbitrary networks of quantum mechanical systems
connected by uni-directional quantum optical fields, and has allowed for a
system theoretic approach to open quantum optics systems. Our aim here is to
establish a network theory for quantum transport systems where typically the
mediating fields between systems are bi-directional. Mathematically this leads
us to study quantum feedback networks where fields arrive at ports in
input-output pairs, which is then just a specially case of the uni-directional
theory. However, it is conceptually important to develop this theory in the
context of quantum transport theory, and the resulting theory extends
traditional approaches which tends to view the components in quantum transport
as scatterers for the various fields, in the process allows us to consider
emission and absorption of field quanta by these components. The quantum
feedback network theory is applicable to both Bose and Fermi fields, moreover
it applies to nonlinear dynamics for the component systems. In this first paper
on the subject, we advance the general theory, but study the case of linear
passive quantum components in some detail.
