Bell State Measurements in Quantum Information Theory and Quantum Foundations

Abstract

A Bell State Measurement is a two-photon measurement that projects the two-photon state represented in a Bell basis into one of the four Bell states. Besides lying at the heart of most protocols in Quantum Information Theory, Bell measurements are also helpful in deepening our understanding of Quantum Theory itself. In the present work, a detailed theoretical and experimental study of Bell State Measurements is undertaken. From a practical side, Bell state measurements are central for the realization of measurement device-independent and device-independent quantum key distribution. Further, One of the earliest foundational questions concerning quantum mechanics is why the quantum state is defined over a complex scalar field and not a real one. Is it possible to rule out 'Real quantum mechanics’ experimentally? Recent work suggests that a Bell State Measurement could provide an answer to this question provisional to certain assumptions. In the later part of the thesis, this question is taken up for investigation. Compared to an earlier work that requires the use of two entangled photon sources, we provide an alternate proof that requires only a single entangled photon source but involves a path-polarization hyper-entangled state.