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 generation^1–4 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 experiments^5–9, 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 expansion^{1–3,10–15}. 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 theorem^4,16,17, we establish security against quantum adversaries. We anticipate that this work will lead to further improvements that push device-independence towards commercial viability.