Fionnuala Curran (ICFO)

One of the most counterintuitive aspects of quantum theory is its claim that there is intrinsic randomness in the physical world. Arising from the phenomenon of superposition, this intrinsic or private randomness is inaccessible to any eavesdropper, a fact that is exploited in the design of quantum random number generators. We investigate how much intrinsic randomness can be extracted from a characterised quantum state using projective measurements. We consider two different quantifiers of randomness: the conditional min-entropy, which is related to the probability that the most powerful quantum eavesdropper can guess the measurement outcomes, and the conditional von Neumann entropy. We find analytic bounds for both of these quantities and necessary and sufficient conditions for a measurement to achieve the bounds. Interesting, while one always can saturate both bounds by measuring in a basis unbiased to that of the quantum state, the conditions for maximising each of the entropies are, in general, inequivalent.