Certifiable Quantum Dice - Or, testable exponential randomness expansion

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.

21 pages, 1 figure. Comments welcome

References in corpus (2)

• Free randomness can be amplified
• Security and Composability of Randomness Expansion from Bell Inequalities

Cited by in corpus (10)

• Fully device independent quantum key distribution
• Security in Quantum Cryptography
• Security of practical private randomness generation
• Security and Composability of Randomness Expansion from Bell Inequalities
• Robust Device-Independent Randomness Amplification with Few Devices
• A Survey of Quantum Property Testing
• The device-independent outlook on quantum physics (lecture notes on the power of Bell's theorem)
• Device-independent randomness amplification with a single device
• Quantum Magic Rectangles: Characterization and Application to Certified Randomness Expansion
• Uncertainty relations for multiple measurements with applications