Randomness is an important in many aspects of our digital lives. Classical random number generators cannot produce genuine randomness as they rely on algorithms or deterministic phenomena. Quantum nonlocality offers a secure way to produce random numbers: Their unpredictability is intrinsic and can be certified just by observing the statistic of the measurement outcomes, without assumptions on how they are produced. For nonlocality, entanglement is necessary. However, entanglement is entirely destroyed after a projective measurement and it cannot be used again, and this fact poses an upper bound to the amount of certified randomness that can be produced from each quantum state with projective measurements. This upper limit can be breached by adopting weak measurements, which allow some entanglement to be maintained and reutilized: in this way an unbounded amount of randomness can be extracted from a single state.

In this work, we study the feasibility of these weak measurements, analyze the robustness to imperfections in the quantum state they are applied to, and then test them using an optical setup based on polarization-entangled photon pairs. We show that the weak measurements are realizable, but can improve the performance of randomness generation only in close-to-ideal conditions.

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