Sequential Semi-Device-Independent Quantum Randomness Certification

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.