archives@tulane.edu / With the advent of lasers the spatial shape of paraxial light also became an avenue for information processing and transfer applications. The light sources that support multiple of these spatial modes as separate, multiplexed information channels are readily used through classical optical implementations such as free-space optical communication, and to enhance the capacity of these channels. Recently, the hot atomic vapour based non-linear optical systems showed promise for the usage of paraxial multiple spatial modes of light for quantum information applications such as quantum communication, quantum networking, quantum computation and various other quantum technologies. In this dissertation, we use analytical, numerical, statistical and experimental techniques to model the propagation of multi-spatial light through various classical and non-linear systems to be able to steer, optimize and control the quantum states generated for quantum technologies applications. In the first chapter, we give a general introduction to classical (both linear & non-linear) and quantum (both linear \& non-linear) optical systems we are going to analyze. In the second chapter, we use a numerical, Fourier transform based beam propagation technique to examine the self-healing of a generic beam that is generated through an atomic process. In the third chapter, we analyzed our hot atomic vapour four-wave mixing experiment that uses a special type of multiple paraxial spatial mode to drive the non-linear optical process through numerical modeling of Fraunhofer diffraction. In the fourth chapter, we devise a coherent, analytically and quantum mechanically motivated beam propagation method based on decomposing the paraxial beam into its constituent multiple spatial modes. We calibrate this method by using the numerical, experimental and theoretical results of the previous chapters to model how the multiple spatial modes propagate through spatial masks that represent apertures, obstructions, atmospheric turbulence. In the fifth chapter, we extend the beam decomposition formalism into semi-classical and full quantum mechanical optical systems to model seeded hot-atomic vapour four-wave mixing experiments. We again calibrate our numerical models of intensity difference squeezing using the previous experimental results. Next, we use these calibrated models to devise a scheme to optimally generate multi-mode squeezed states. Lastly, in the sixth chapter, we turn our attention into estimating the quantum state of discrete variable, polarization qubit systems using machine learning and various other stochastic techniques. We improve these well studied systems to detect the quantum states in real time, in the presence of noise, and in the absence of various measurements using machine learning. We study these discrete variable, polarization qubit systems both as a gateway and a complement to study the tomographic reconstruction of continuous variable quantum optical systems of the previous chapters, in order to achieve our general goal of having a general estimation, steering and control methodology for quantum networking applications. / 1 / ONUR DANACI