Studies in Applied and Fundamental Quantum Mechanics: Duality, Tomography, Cryptography and Holography

Abstract

This thesis encompasses a collection of four pieces of work on wave-particle duality, weak-value-assisted tomography, high-dimensional quantum key distribution, and phase-only holograms. In the work on duality, we derive a novel duality relation, and we sketch a thought experiment that leads to an apparent violation of the duality principle. In the project on tomography, we perform a state determination procedure with weak values, and we study the accuracy of the method. In the quantum cryptography project, we optimize an experimental implementation of a quantum cryptography system where two parties share information with the orbital angular momentum degree of freedom of entangled photon pairs. Finally, in the work on holography, we establish the exact solution to the encryption of a phase-only hologram, and experimentally demonstrate its application to spatial light modulators. The four projects provide improvements on measurement procedures in applied and fundamental quantum mechanics.