BEGIN:VCALENDAR VERSION:2.0 PRODID:Icfo X-PUBLISHED-TTL:P1W BEGIN:VEVENT UID:6ab28c09b4477 DTSTART:20261030T090000Z SEQUENCE:0 TRANSP:OPAQUE LOCATION:ICFO Auditorium SUMMARY:ICFO | FIONNUALA CURRAN CLASS:PUBLIC DESCRIPTION:The unpredictability of quantum physics gives rise to an intrin sic form of randomness. We generate it by performing a measurement on a qu antum state. In an adversarial scenario\, we then quantify the randomness by the probability that a correlated eavesdropper could correctly guess th e measurement outcomes. This thesis addresses the following question: give n a known quantum state and measurement\, how much intrinsic randomness ca n we generate?\nWe begin by solving the maximal intrinsic randomness of an y state\, optimised over all projective measurements\, for four figures of merit: the conditional min\, max and von Neumann entropies\, and the newl y introduced unambiguous randomness. The last of these describes an eavesd ropper who is never wrong\, but can sometimes return an inconclusive outco me. Relaxing the assumption of perfect accuracy\, we also consider randomn ess given a fixed rate of inconclusive outcomes. We solve both of these qu antities for any state and projective measurement in dimension two. If the setup is used to choose random bases for a prepare-and-measure quantum ke y distribution protocol\, we show that the unambiguous randomness captures the knowledge gained by an eavesdropper about the secret key\, without ca using any disturbance. We then turn to extremal measurements beyond the pr ojective case\, which may have more outcomes. An unbiased measurement is o ne whose outcomes all have the same a priori probability. We characterise the randomness generated by any unbiased extremal rank-one measurement act ing on any state\, solving the problem explicitly in dimension two. Four-o utcome measurements of this type are tomographic\, such that one can fully determine the state from the outcome probabilities\, so these results hol d for fully source-device-dependent randomness too. The tetrahedral symmet ric informationally complete (SIC) measurement\, we find\, has the least i ntrinsic randomness within this class. We also present the biased skewed S IC family of measurements\, and use them to prove that 2 log d bits of ran domness\, the maximal amount\, can be generated device-dependently (or sou rce-device-independently) in any dimension d in which there exists a SIC m easurement.Reversing the scenario\, we optimise over all states to solve t he maximal intrinsic randomness of two classes of non-extremal\, or noisy\ , measurements: any two-outcome measurement in dimension two\, and project ive measurements in any dimension affected by isotropic noise. In a realis tic implementation\, however\, neither the state nor the measurement is co mpletely free of noise. Taking a simple example of a state measured in a b asis of any dimension\, we compare the case where only one device is affec ted by noise to that where both devices are noisy\, such that an eavesdrop per may have joint correlations with the state and the measurement. For a fixed amount of total noise\, we find that\, contrary to the common practi ce of attributing all experimental noise to a single device\, the joint-no ise eavesdropper strictly outperforms her single-noise counterpart\, compr omising the security of the randomness generated.That the outcomes of a qu antum measurement are unpredictable has been known since the inception of quantum theory. This thesis presents a step forward in analytically charac terising the intrinsic randomness of quantum physics. On the practical sid e\, our results bound the functionality of quantum random number generator s\, under various assumptions. On a more foundational level\, this work pr ovides a new lens through which to compare quantum states and measurements and\, from their vast landscape\, to see which of them emerge as the most random.\nThesis Director: Prof. Dr. Antonio Ací\;n DTSTAMP:20260922T140913Z END:VEVENT END:VCALENDAR