Increased Certification of Semi-device Independent Random Numbers using Many Inputs and More Postprocessing

TL;DR

This paper explores how increasing input settings and advanced postprocessing in semi-device independent quantum experiments can enhance certified randomness, despite higher computational demands, offering a practical route to improve quantum randomness generation.

Contribution

It demonstrates that more certified randomness can be achieved by dedicating additional inputs and developing methods to reduce computational complexity in semi-device independent protocols.

Findings

More input settings lead to higher certified randomness.

Enhanced postprocessing increases randomness certification.

A new method reduces computational complexity of certification.

Abstract

Quantum communication with systems of dimension larger than two provides advantages in information processing tasks. Examples include higher rates of key distribution and random number generation. The main disadvantage of using such multi-dimensional quantum systems is the increased complexity of the experimental setup. Here, we analyze a not-so-obvious problem: the relation between randomness certification and computational requirements of the postprocessing of experimental data. In particular, we consider semi-device independent randomness certification from an experiment using a four dimensional quantum system to violate the classical bound of a random access code. Using state-of-the-art techniques, a smaller quantum violation requires more computational power to demonstrate randomness, which at some point becomes impossible with today's computers although the randomness is (probably) still there. We show that by dedicating more input settings of the experiment to randomness certification, then by more computational postprocessing of the experimental data which corresponds to a quantum violation, one may increase the amount of certified randomness. Furthermore, we introduce a method that significantly lowers the computational complexity of randomness certification. Our results show how more randomness can be generated without altering the hardware and indicate a path for future semi-device independent protocols to follow.