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 × 10 8 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. Device-independent randomness expansion is demonstrated in an experiment that is secure against quantum adversaries as established by the entropy accumulation theorem.