Device-independent randomness generation from several Bell estimators

TL;DR

This paper develops protocols for device-independent randomness generation that utilize multiple Bell estimators or full measurement data, achieving optimal randomness without assuming violation of a specific Bell inequality.

Contribution

It introduces new protocols that estimate multiple Bell expressions or use full outcome frequencies for randomness generation, improving accuracy and security.

Findings

Achieves asymptotically optimal randomness generation from experimental data.

Does not require prior assumption of Bell inequality violation.

Ensures security against classical side information.

Abstract

Device-independent randomness generation and quantum key distribution protocols rely on a fundamental relation between the non-locality of quantum theory and its random character. This relation is usually expressed in terms of a trade-off between the probability of guessing correctly the outcomes of measurements performed on quantum systems and the amount of violation of a given Bell inequality. However, a more accurate assessment of the randomness produced in Bell experiments can be obtained if the value of several Bell expressions is simultaneously taken into account, or if the full set of probabilities characterizing the behavior of the device is considered. We introduce protocols for device-independent randomness generation, secure against classical side information, that rely on the estimation of an arbitrary number of Bell expressions or even directly on the experimental frequencies of measurement outcomes. Asymptotically, this results in an optimal generation of randomness from experimental data (as measured by the min-entropy), without having to assume beforehand that the devices violate a specific Bell inequality.