Presentation of Ph.D. Thesis

Interferometry has played a pivotal role in testing the fundamental theories of quantum mechanics, precision metrology and the development of advanced quantum technologies. In this thesis, we explore the application of interferometric methodologies in two distinct aspects, the characterization of unknown quantum states and the determination of non-classical measures associated with quantum systems. The works combine theoretical discussions to highlight the operational principles of proposed schemes with experimental implementations in optical setups to demonstrate their feasibility for photonic systems. Employing interferometry as a tool, we introduce a novel state determination technique called Quantum State Interferography (QSI), that characterizes an indeterminate quantum state by analyzing the interference patterns produced in a single setup. We experimentally implement the scheme in a two path interferometer to characterize the polarization qubits of light and assess the efficacy of this method by computing the fidelity of the reconstructed states. We extend this protocol to characterize the pure qudits (d > 2) and pure bipartite qubits as well. QSI is highlighted as a scheme for single-shot characterization of qubits and pure qudits, as well as for quantifying entanglement in pure bipartite qubits. Furthermore, we explore interferometric techniques to establish the non-classical nature of the `generalized probability’ or the quantum measure within the context of Quantum Measure Theory. We present an experimental realization of a two site hopper in an optical setup to infer the quantum measure for a specific hopper event using the method of event-filtering, which could lead to the future tests on foundational aspects of quantum theory.