Roger Colbeck

Recent advancements in device-independent randomness expansion (DIRE) protocols have shown significant improvements in random bit generation rates yet remain slower than other methods. Optical systems, ideal for long-distance quantum information transmission, face challenges due to noisy photon sources and inefficient detectors, resulting in lower randomness rates of photonics-based DIRE implementations. In this work, we demonstrate how to tune DIRE protocols and the underlying Bell tests to specific noise levels, thereby enhancing the extractable randomness in photonics-based DIRE implementations.

Nonlocal tests on multipartite quantum correlations can certify randomness in a device-independent (DI) way. Such correlations admit a rich structure, making the task of choosing an appropriate witness, known as a Bell inequality, difficult. For example, extremal Bell inequalities are tight witnesses of nonlocality, however achieving their maximum violation places constraints on the underlying quantum system, which are often incompatible with optimal randomness generation. As a result we find a trade-off between maximum randomness and Bell violation. Understanding this trade-off for more than two parties has not been explored, and would inform the best way to generate DI randomness in this setting. Moreover, suitable techniques that enable maximum randomness certification for arbitrarily many parties are missing. Here, we study the maximum amount of randomness that can be certified by correlations exhibiting a violation of the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality. We find that maximum quantum violation and maximum randomness are incompatible for any even number of parties, with incompatibility diminishing as the number of parties grow, and conjecture the precise trade-off. We also show that maximum MABK violation is not necessary for maximum randomness for odd numbers of parties. To obtain our results, we derive new families of Bell inequalities certifying maximum randomness from a new technique for randomness certification, which we call "expanding Bell inequalities". Our technique allows one to take a bipartite Bell expression, known as the seed, and transform it into a multipartite Bell inequality tailored for randomness certification, showing how intuition learned in the bipartite case can find use in more complex scenarios.