Benchmarking weak randomness in Quantum and Natural Sources
Maciej Stankiewicz, Roberto Salazar, Mikołaj Czechlewski, Alejandra Muñoz Jensen, Catalina Morales-Yáñez, Omer Sakarya, Julio Viveros Carrasco, Stephen Walborn, Gustavo Lima, Karol Horodecki
TL;DR
This work addresses certifying private randomness when sources are potentially weak, using an axiomatic framework to estimate the Santha–Vazirani parameter ε from finite data. It introduces SVTest, an open-source tool that computes history-dependent ε_h from real-valued sequences after discretization and aggregates them into a single ε via weighted averages guided by four axioms. The authors apply the framework to a commercial quantum RNG and to seismic data, showing that the RNG yields near-ideal SV randomness while seismic waveforms and ambient noise exhibit measurable SV-type randomness that depends strongly on discretization and data type. These results reveal seismic phenomena as a viable, publicly available randomness source and provide a practical path to quantum randomness amplification using natural sources, with broad implications for cryptography and device-independent randomness protocols.
Abstract
Private randomness is a fundamental resource for cryptography, security proofs, and information processing. Quantum devices offer a unique advantage by amplifying weak randomness sources in regimes unattainable by classical means. A central theoretical model for such sources is the Santha-Vazirani (SV) model, yet identifying natural processes that satisfy this model remains a major challenge. Here we take three steps toward addressing this problem. First, we introduce an axiomatic framework for quantifying weak randomness, providing a unified basis for estimating an SV-type source. Second, we develop SVTest, a general-purpose software tool for estimating the SV parameter of an arbitrary data sequence. Third, we apply this framework to both engineered and natural sources. Using data from a self-certifying commercial quantum random number generator with guaranteed min-entropy as a benchmark, we validate the accuracy and limitations of our estimation method. We then analyze geophysical signals associated with seismic activity and find that, depending on the discretization, both earthquakes and local seismic noise can exhibit SV-type randomness. Our results indicate that geophysical phenomena may constitute viable sources of cryptographic randomness, establishing an unexpected connection between quantum information theory and geophysics.