  Currently, optical technology impacts most of our lives, from light used in
scientific measurement to the fiber optic cables that makeup the backbone of
the internet. However, as our current optical infrastructure grows, we discover
that these technologies are not limitless. However, our current optical
technology functions on classical principles, and can be easily improved by
incorporating our knowledge of quantum optics. In order to implement quantum
technologies, our understanding of quantum coherence must improve. Through this
knowledge we can maintain quantum states, and therefore their information,
longer. In this dissertation, I will demonstrate that with sufficient knowledge
of coherent properties, a simple algebra can be derived which can provide rules
for graph reductions on a quantum network graph. Using this knowledge, I then
provide a rudimentary algorithm which can find the optimal subgraph for
communication on a quantum network. Next, I demonstrate that by measuring the
photon statistics and second-order quantum coherence of a field, one can create
a neural network capable of distinguishing the light sources on a pixel. Which
is then applied to develop an imaging scheme capable of surpassing the
Abbe-Rayleigh Criterion. Lastly, I present a multiphoton quantum version of the
van Cittert-Zernike theorem. This provides formalism capable of determining the
propagation of quantum coherence throughout a system. I then demonstrate the
usefulness of the theorem by demonstrating sub-Poissonian statistics created by
a linear system with an incident thermal beam, obtainable only by
post-selection. Altogether, this provides incite into new applications of
coherence to quantum technologies and the formalism to extending our knowledge
even further.
