Sequential Semi-Device-Independent Quantum Randomness Certification

TL;DR

This paper develops a framework for certifying quantum randomness through sequential measurements, demonstrating that maximum confidence measurements can generate and verify randomness even under adaptive attacks.

Contribution

It introduces a general method to bound certifiable randomness in sequential quantum measurements using semidefinite programming and entropy accumulation techniques.

Findings

Sequential measurements can certify randomness across multiple steps.

Maximum confidence measurements enable distribution of certified randomness.

The framework is robust against adaptive adversarial strategies.

Abstract

Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the context of semi-device-independent randomness certification using sequential maximum confidence measurements. We develop a general framework and versatile numerical methods to bound the amount of certifiable randomness in such scenarios. We further introduce a technique to compute min-tradeoff functions via semidefinite programming duality, thus making the framework suitable for bounding the certifiable randomness against adaptive attacking strategies through entropy accumulation. Our results establish sufficient criteria showing that maximum confidence measurements enable the distribution and certification of randomness across a sequential measurement chain.