The ability to produce random numbers that are unknown to any outside party is crucial for many applications. Device-independent randomness generation^1,2,3,4 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^5,6,7,8,9, 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^{1,2,3,10,11,12,13,14,15}. 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 × 10⁸ 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.

生成任何外部方都不知道的随机数的能力对于许多应用程序来说都是至关重要的。与设备无关的随机性生成^{1、2、3、4}不需要受信任的设备，因此为输出的安全性提供了强有力的保证，但其代价是需要违反贝尔不等式来实现。另一个挑战是使安全证明中的界限足够严格，以允许使用当代技术进行随机扩展。尽管在最近的实验^5,6,7,8,9中产生了随机性，但这样做所消耗的随机性量太高，无法根据现有理论证明扩展。在这里，我们展示了一个实验，展示了与设备无关的随机性扩展^{1,2,3,10,11,12,13,14,15}。通过开发单光子检测效率约为 84% 的贝尔测试装置并使用抽查协议，我们实现了 2.57 × 10 ⁸认证比特的净增益，稳健性误差为 3.09 × 10 ^-12。实验运行了 19.2 小时，这对应于每秒 13,527 位的平均随机生成速率。通过发展熵积累定理^4,16,17，我们建立了对抗量子对手的安全性。我们预计这项工作将导致进一步的改进，将设备独立性推向商业可行性。