Applications of hybrid measurements with discrete and continuous variables

The main topic of this thesis revolves around quantum measurement. We illustrate how two different views of quantum objects, the discrete-and continuous-variable views, can be combined to more effectively distinguish between orthogonal states. Such combined measurements are referred to as hybrid. The discrete-variable view is more appropriate to probe energy eigenstates. However, when two or more energy eigenstates are superposed, accurate measurements in the energy eigenbasis require rotations in phase space which are very unwieldy as they require strong nonlinearities and
elaborate interactions between light and matter. On the other hand, energy eigenstate superpositions carry a continuous relative phase which is easily probed by continuous-variable interference measurements such as homodyning. The tradeoff between photon counting and homodyning is in practice determined by feasibility studies. This is what we do for two particular applications of quantum measurements: Bell tests and the amplication of Schrödinger cat states. This project also had an experimental component which was supposed to produce high-fidelity Schrödinger cat states. This
goal turned out to be hampered by noise from the laser as well as a series of anomalous behavior of the nonlinear crystal whereby no classical de-amplification, and therefore no squeezing, could be observed.