Device-independent randomness expansion with entangled photons

With the growing availability of experimental loophole-free Bell tests^1–5, it has become possible to implement a new class of device-independent random number generators whose output can be certified^6,7 to be uniformly random without requiring a detailed model of the quantum devices used^8–10. However, all these experiments require many input bits to certify a small number of output bits, and it is an outstanding challenge to develop a system that generates more randomness than is consumed. Here we devise a device-independent spot-checking protocol that consumes only uniform bits without requiring any additional bits with a specific bias. Implemented with a photonic loophole-free Bell test, we can produce 24% more certified output bits (1,181,264,237) than consumed input bits (953,301,640). The experiment ran for 91.0 h, creating randomness at an average rate of 3,606 bits s^–1 with a soundness error bounded by 5.7 × 10⁻⁷ in the presence of classical side information. Our system allows for greater trust in public sources of randomness, such as randomness beacons¹¹, and may one day enable high-quality private sources of randomness as the device footprint shrinks.