Certifiable Quantum Dice - Or, testable exponential randomness expansion

TL;DR

This paper presents a protocol for generating a large amount of certifiable true randomness using quantum devices, with minimal seed randomness and security against quantum adversaries, based on simple statistical tests and no-signaling assumptions.

Contribution

It introduces a new protocol for exponential randomness expansion that is certifiable and secure against quantum adversaries, requiring only minimal initial randomness.

Findings

Generates n bits of randomness from O(log n) seed bits

Certifies randomness using simple statistical tests

Secure against adversaries with prior entanglement

Abstract

We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n bits of true randomness from a seed of O(log n) uniform bits. The bits generated are certifiably random based only on a simple statistical test that can be performed by the user, and on the assumption that the devices obey the no-signaling principle. No other assumptions are placed on the devices' inner workings. A modified protocol uses a seed of O(log^3 n) uniformly random bits to generate $n$ bits of true randomness even conditioned on the state of a quantum adversary who may have had prior access to the devices, and may be entangled with them.