Universal security for randomness expansion

We show that any spatially separated multi-part quantum device demonstrating nonlocality can be used in an untrusted-device protocol for randomness expansion with unconditional quantum security. A consequence is that the noise tolerance for secure randomness expansion only needs to be small enough that it rules out deterministic behavior of the device. This greatly reduces the requirement on implementation precision. For example, for the CHSH game, the noise can be 10.3%, compared with 1.5% in the previous bound. We also show that similar results hold with nonlocality replaced by the broader concept of contextuality, and the spatial separation requirement replaced by the broader compatibility requirement. This is the first full quantum security proof for contextuality-based randomness expansion. For both nonlocality and contextuality, we have identified the minimum device requirement. Our results imply in particular the equivalence of quantum security with classical security for the protocols considered. Our main technical contribution is a strong Schatten-norm uncertainty principle which applies to arbitrary pairs of noncommuting binary measurements.