Characterizing high-dimensional optical systems with applications in compressive sensing and quantum data locking

Thesis (Ph. D.)--University of Rochester. Department of Physics and Astronomy, 2018.High-dimensional systems are desired for their ability to transfer large amounts of information. This dissertation focuses on the characterization and usage of high-dimensional optical systems for computational imaging, high-dimensional entanglement, and efficient secure-information transfer. Within computational imaging systems, capturing the most spatial frequencies results in sharper images. Utilizing the correlations within high-dimensional entanglement offers signal-to-noise ratio enhancements over lowlight imaging and spectroscopic systems. Finally, high-dimensional quantum channels offer a regime in which quantum data locking can encrypt information according to information-theoretic-secure standards more efficiently than classical systems. While high-dimensionality offers certain performance gains, characterizing and then harnessing high-dimensional systems for computational imaging, entanglementenhanced applications, and quantum-secure direct communication can be prohibitively difficult. This dissertation offers unique solutions to each of these problems. Compressive imaging is relied on heavily to improve measurement rates in limitedresource imaging systems. As such, compressive sensing is introduced in chapter 1 while entanglement and an experimental source of high-dimensional entangled photons is covered in chapter 2. Chapter 3 introduces Sylvester-Hadamard matrices for compressive measurement and efficient computational-recovery of high-dimensional correlations. Compressive imaging is then presented as an efficient means of converting a standard frequency-modulated continuous-wave LiDAR system into a high-resolution depth-imaging system in chapter 4. Chapter 5 introduces quantum data locking and presents one of the first experimental demonstrations made possible by the use of a large-area, high-efficiency, single-photon-counting detector array. For completeness, robust compressive sensing recovery algorithms using the alternating direction method of multipliers are presented in the appendix