From prepare-and-measure scenarios to certified quantum randomness
quantum information; prepare-and-measure; certified randomness; semi-device-independent.
Prepare-and-measure scenarios offer a simple and experimentally accessible framework to investigate nonclassical behavior. Within this context, the goal of this master's thesis is to develop this formalism from both conceptual and technical perspectives. We aim to define more precisely what we mean by randomness, understand how it emerges in prepare-and-measure scenarios, and ultimately show how it can be certified through so-called dimension witnesses. The work is developed within a semi-device-independent regime, in which no detailed knowledge of the internal functioning of the devices is assumed, but only the dimension of the communicated system. In this setting, we show how violations of dimension witnesses can be converted into quantitative guarantees about the randomness generated. Beyond organizing and presenting the foundations of this formalism, the work also seeks to connect it to established continuous-variable optical measurement techniques. We show that realistic and relatively simple setups, based on homodyne and displacement measurements, are already sufficient to produce violations capable of certifying quantum randomness, even in the presence of losses and finite detection efficiency. The overall goal is to show that practical and scalable quantum randomness generation can be achieved in simple continuous-variable experiments.