  Recently, our group has demonstrated an ultrafast, low-loss, fiber-loop
switch based on a nonlinear Sagnac-interferometer design, using which entangled
photons were shown to be routed without any measurable degradation in their
entanglement fidelity [Hall {\it et al.}, Phys. Rev. Lett. {\bf 106}, 053901
(2011)]. Such a device represents an enabling technology for a rich variety of
networked quantum applications. In this paper we develop a comprehensive
quantum theory for such switches in general, i.e., those based on nonlinear
Sagnac interferometers, where the in-coupling of quantum noise is carefully
modeled. Applying to the fiber-loop switch, the theory shows good agreement
with the experimental results without using any fitting parameter. This theory
can serve as an important guiding tool for configuring switches of this kind
for future quantum networking applications.
