Maximal device-independent randomness in every dimension

TL;DR

This paper demonstrates that the maximum amount of device-independent randomness, proportional to the quantum system's dimension, can be achieved in all dimensions using explicit protocols and new certification techniques.

Contribution

It introduces explicit protocols that attain the maximum randomness bound for any dimension and develops new certification methods for device-independent scenarios.

Findings

Maximum randomness bound of 2 log(d) bits achieved for all dimensions d

Explicit protocols provided for extracting optimal randomness

New certification techniques developed for complex device-independent scenarios

Abstract

Random numbers are used in a wide range of sciences. In many applications, generating unpredictable private random numbers is indispensable. Device-independent quantum random number generation is a framework that makes use of the intrinsic randomness of quantum processes to generate numbers that are fundamentally unpredictable according to our current understanding of physics. While device-independent quantum random number generation is an exceptional theoretical feat, the difficulty of controlling quantum systems makes it challenging to carry out in practice. It is therefore desirable to harness the full power of the quantum degrees of freedom (the dimension) that one can control. It is known that no more than $2 \log(d)$ bits of private device-independent randomness can be extracted from a quantum system of local dimension $d$. In this paper we demonstrate that this bound can be achieved for all dimensions $d$ by providing a family of explicit protocols. In order to obtain our result, we develop new certification techniques that can be of wider interest in device-independent applications for scenarios in which complete certification ('self-testing') is impossible or impractical.