Randomness Extraction from Bell Violation with Continuous Parametric Down-Conversion

Abstract

We present a violation of the Clauser-Horne-Shimony-Holt inequality without the fair sampling assumption with a continuously pumped photon pair source combined with two high efficiency superconducting detectors. Because of the continuous nature of the source, the choice of the duration of each measurement round effectively controls the average number of photon pairs participating in the Bell test. We observe a maximum violation of $S=2.01602(32)$ with an average number of pairs per round of $\approx 0.32$, compatible with our system overall detection efficiencies. Systems that violate a Bell inequality are guaranteed to generate private randomness, with the randomness extraction rate depending on the observed violation and on the repetition rate of the Bell test. For our realization, the optimal rate of randomness generation is a compromise between the observed violation and the duration of each measurement round, with the latter realistically limited by the detection time jitter. Using an extractor composably secure against quantum adversary with quantum side information, we calculate an asymptotic rate of $\approx 1300\mathrm{random}\mathrm{bits}/\mathrm{s}$. With an experimental run of 43 min, we generated 617 920 random bits, corresponding to $\approx 240\mathrm{random}\mathrm{bits}/\mathrm{s}$.