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Quantum nonlocality offers a secure way to produce random numbers: theirunpredictability is intrinsic and can be certified just by observing thestatistic of the measurement outcomes, without assumptions on how they areproduced. To do this, entangled pairs are generated and measured to violate aBell inequality with the outcome statistics. However, after a projectivequantum measurement, entanglement is entirely destroyed and cannot be usedagain. This fact poses an upper bound to the number of random numbers that canbe produced from each quantum state when projective measurements are employed.Instead, by using weak measurements, some entanglement can be maintained andreutilized, and a sequence of weak measurements can extract an unbounded amountof randomness from a single state as predicted in Phys. Rev. A 95, 020102(R)(2017). We study the feasibility of these weak measurements, analyze therobustness to imperfections in the quantum state they are applied to, and thentest them using an optical setup based on polarization-entangled photon pairs.We show that the weak measurements are realizable, but can improve theperformance of randomness generation only in close-to-ideal conditions.

Experimental Test of Sequential Weak Measurements for Certified Quantum Randomness Extraction