Quantum state discrimination with applications in contextuality and randomness certification

The theory of quantum mechanics establishes that some physical behaviors depart drastically from the classical world we are all used to. For instance, two different state preparations on the same physical system, in general,
cannot be perfectly distinguishable. This statement motivates the question of how well quantum states can be discriminated, which is the main study of quantum state discrimination. In this thesis, I investigate two important branches of quantum information science from the perspective of quantum state discrimination.
The first is quantum randomness. Randomness plays an important role in cryptography, where unpredictability is central. Here, I present a surprisingly simple protocol to generate more than one bit of certified randomness per round in a qubit prepare-and-measure scenario. The protocol is also implemented and experimentally tested in an optical platform. The second is quantum contextuality. Contextuality is a fundamental property of quantum mechanics which states that the distribution of measurement outcomes of a physical system depends not only on its state, but also on the context in which it is measured. In this thesis I propose a noise-robust contextuality witness based on optimal two-state discrimination. Moreover, I explore contextual advantages in state discrimination tasks versus noncontextual models, which can be seen as representing classical physics.
Throughout this thesis, I center on maximum confidence discrimination, a state discrimination protocol with the goal of maximizing the confidence. That is, the probability that the state preparation is indeed the one indicated by the measurement outcome. From this perspective, I compare the power of quantum and noncontextual models in terms of randomness certification. Our results report that the certified randomness in a quantum framework is greater than in the noncontextual model, as long as the adversary is quantum in both cases.