Maximal quantum randomness in Bell tests

TL;DR

This paper demonstrates how symmetries in Bell inequalities and unique quantum distributions can certify maximal local and global randomness in Bell tests, including N-party scenarios achieving N perfect random bits.

Contribution

It introduces a simple symmetry-based argument to certify maximal randomness and proves the existence of N-party Bell tests with maximal global randomness.

Findings

Symmetries in Bell inequalities can certify maximal randomness.

Unique quantum distributions maximally violate Bell inequalities.

Existence of N-party Bell tests with N perfect random bits.

Abstract

The non-local correlations exhibited when measuring entangled particles can be used to certify the presence of genuine randomness in Bell experiments. While non-locality is necessary for randomness certification, it is unclear when and why non-locality certifies maximal randomness. We provide here a simple argument to certify the presence of maximal local and global randomness based on symmetries of a Bell inequality and the existence of a unique quantum probability distribution that maximally violates it. Using our findings, we prove the existence of N-party Bell test attaining maximal global randomness, that is, where a combination of measurements by each party provides N perfect random bits.