Device-independent randomness amplification with a single device

TL;DR

This paper presents a method to amplify weak randomness using a single quantum device with GHZ entanglement, producing perfect random bits from sources previously considered unusable.

Contribution

It introduces a novel protocol for randomness amplification with a single, non-communicating quantum device, effective even for sources below classical extractability thresholds.

Findings

Achieves perfect randomness from weak sources with a specific entropy threshold.

Utilizes a single device decomposable into three parts for repeated amplification.

Works with sources unexploitable by classical or existing quantum methods.

Abstract

Expansion and amplification of weak randomness with untrusted quantum devices has recently become a very fruitful topic of research. Here we contribute with a procedure for amplifying a single weak random source using tri-partite GHZ-type entangled states. If the quality of the source reaches a fixed threshold $R=\frac{1}{4}\log_{2}(10)$, perfect random bits can be produced. This technique can be used to extract randomness from sources that can't be extracted neither classically, nor by existing procedures developed for Santha-Vazirani sources. Our protocol works with a single fault-free device decomposable into three non-communicating parts, that is repeatedly reused throughout the amplification process.