Certifying the inherent randomness in quantum state discrimination

Quantum mechanics forbids perfect discrimination of non-orthogonal states, a limitation that can be exploited to certify intrinsic randomness. Building on this principle, this thesis investigates how limits on state discrimination can be used to generate certified randomness in prepare-and-measure protocols. In particular, we study how the performance of minimum-error quantum state discrimination constrains an adversary’s ability to predict measurement outcomes, under the sole assumption of an average energy constraint on the prepared states. We show how observed discrimination performance bounds an adversary’s optimal guessing probability and yields certified min-entropy. Exact results are obtained for fixed-dimension qubit ensembles, including closed-form expressions for two-qubit preparations and extensions to general qubit ensembles. We then introduce dimension-unbounded semidefinite programming relaxations based on Gram-matrix techniques, providing device-independent bounds that rely only on the energy constraint. A central result is the identification of critical discrimination thresholds beyond which deterministic strategies are excluded and genuine quantum randomness is certified. These results establish quantum state discrimination as an operational witness for randomness generation under natural physical assumptions.