Device-independent randomness expansion against quantum side information

The ability to produce random numbers that are unknown 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 output, but it comes at price requiring violation a Bell inequality implementation. A further challenge make bounds in proofs tight enough allow expansion with contemporary technology. Although has been generated recent experiments5–9, amount consumed doing so too high certify based on existing theory. Here we present an experiment demonstrates device-independent expansion1–3,10–15. By developing test setup single-photon detection efficiency around 84% by using spot-checking protocol, achieve net gain 2.57 × 108 certified bits soundness error 3.09 10−12. ran 19.2 h, which corresponds average rate generation 13,527 per second. entropy accumulation theorem4,16,17, establish against quantum adversaries. We anticipate this work will lead improvements push device-independence towards commercial viability. demonstrated secure adversaries as established theorem.