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 (DIRNG) allows new randomness to be provably generated, without needing to trust the devices used for the protocol. This provides strong guarantees about the security of the output, but comes at the price of requiring the violation of a Bell inequality to implement. A further challenge is to make the bounds in the security proofs tight enough to allow expansion with contemporary technology. Thus, while randomness has been generated in recent experiments, 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 (DIRNE), i.e., where the generated randomness surpasses that consumed. By developing a loophole-free Bell test setup with a single photon detection efficiency of around 81% and exploiting a spot-checking protocol, we achieve a net gain of $2.63\times10^8$ certified bits with soundness error $5.74\times10^{-8}$. The experiment ran for 220 hours corresponding to an average rate of randomness generation of 8202 bits/s. By developing the Entropy Accumulation Theorem (EAT), we established security against quantum adversaries. We anticipate that this work will lead to further improvements that push device-independence towards commercial viability.