Deterministic randomness extraction for quantum random number generation with partial trust

TL;DR

This paper extends deterministic randomness extractors to quantum sources with partial trust, enabling secure quantum randomness generation in practical scenarios with minimal assumptions, and demonstrates positive key rates in simulations.

Contribution

It adapts existing deterministic extractors for quantum sources to partial trust and semi-device-independent settings, broadening their applicability.

Findings

Extractors are effective under partial trust conditions.

Positive key rates achieved with 7,000+ rounds in simulations.

Applicable to prepare-and-measure quantum scenarios.

Abstract

It is a well-known fact in classical information theory that no deterministic procedure can extract close-to-ideal randomness from an arbitrary entropy source. On the other hand, if additional knowledge about the source is available -- e.g., that it is a sequence of independent Bernoulli trials -- then deterministic extractors do exist. For quantum entropy sources, where in addition to classical random variables we consider quantum side information, the use of extra knowledge about their structure was pioneered in a recent publication [C. Foreman and L. Masanes, Quantum 9, 1654 (2025)]. In that work, the authors provide deterministic extractors for device-independent randomness generation with memoryless devices achieving a sufficiently high CHSH score. In this work, we port their construction to the prepare-and-measure scenario. Specifically, we prove that the considered functions are also extractors for memoryless devices in settings with partial trust, either in the state preparation or in the measurement, as well as in a semi-device-independent setting under an overlap assumption on the prepared quantum states. Within this last setting, we simulate the resulting randomness generation protocol on a novel and experimentally relevant family of behaviors, observing positive key rates already for $7\times 10^3$ rounds.