Free randomness can be amplified

TL;DR

This paper demonstrates that partially free random bits can be amplified to nearly perfectly free bits using principles based solely on no-signalling, challenging assumptions about the necessity of perfect randomness in quantum experiments.

Contribution

It introduces a method to amplify weakly free random bits into nearly perfect ones under no-signalling constraints, relaxing the assumption of perfect free randomness.

Findings

Partially free random bits can be amplified to near-perfect free bits.

The procedure relies only on the no-signalling principle.

Conjecture that such amplification exists for all non-trivial thresholds.

Abstract

Are there fundamentally random processes in nature? Theoretical predictions, confirmed experimentally, such as the violation of Bell inequalities, point to an affirmative answer. However, these results are based on the assumption that measurement settings can be chosen freely at random, so assume the existence of perfectly free random processes from the outset. Here we consider a scenario in which this assumption is weakened and show that partially free random bits can be amplified to make arbitrarily free ones. More precisely, given a source of random bits whose correlation with other variables is below a certain threshold, we propose a procedure for generating fresh random bits that are virtually uncorrelated with all other variables. We also conjecture that such procedures exist for any non-trivial threshold. Our result is based solely on the no-signalling principle, which is necessary for the existence of free randomness.