With the growing availability of experimental loophole-free Bell tests^1,2,3,4,5, 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^8,9,10. 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.

随着实验性无漏洞贝尔测试^1,2,3,4,5的日益普及，有可能实现一类新的与设备无关的随机数生成器，其输出可以证明^6,7是一致随​​机的，无需需要使用的量子设备的详细模型^8,9,10. 然而，所有这些实验都需要许多输入位来验证少量输出位，开发一个产生比消耗更多随机性的系统是一个突出的挑战。在这里，我们设计了一个独立于设备的抽查协议，它只使用统一的比特，而不需要任何具有特定偏差的额外比特。通过光子无漏洞贝尔测试实施，我们可以产生比消耗的输入比特 (953,301,640) 多 24% 的认证输出比特 (1,181,264,237)。实验运行了 91.0 小时，在存在经典边信息的情况下，以 3,606 位 s ^–1的平均速率产生随机性，健全性误差以 5.7 × 10 ^-7为界。我们的系统允许更大程度地信任公共随机源，例如随机信标¹¹，并且有朝一日随着设备占用空间的缩小，可能会启用高质量的私人随机源。