Device-independent randomness expansion against quantum side information

The ability to produce random numbers that are unknown to any outside party is crucial for many applications. Device-independent randomness generation1–4 does not require trusted devices and therefore provides strong guarantees of the security of the output, but it comes at the price of requiring the violation of a Bell inequality for implementation. A further challenge is to make the bounds in the security proofs tight enough to allow randomness expansion with contemporary technology. Although randomness has been generated in recent experiments5–9, the amount of randomness consumed in doing so has been too high to certify expansion based on existing theory. Here we present an experiment that demonstrates device-independent randomness expansion1–3,10–15. By developing a Bell test setup with a single-photon detection efficiency of around 84% and by using a spot-checking protocol, we achieve a net gain of 2.57 × 108 certified bits with a soundness error of 3.09 × 10−12. The experiment ran for 19.2 h, which corresponds to an average rate of randomness generation of 13,527 bits per second. By developing the entropy accumulation theorem4,16,17, we establish security against quantum adversaries. We anticipate that this work will lead to further improvements that push device-independence towards commercial viability. Device-independent randomness expansion is demonstrated in an experiment that is secure against quantum adversaries as established by the entropy accumulation theorem.