Algebraic Symmetry and Stochastic Independence: A Comparative Study of Deterministic, Seeded, and Matrix-based Randomness Extraction on QRNG-Generated Datasets

Theoretically, Quantum random number generators (QRNGs) can produce truly random numbers that cannot be predicted in advance and have numerous uses. But in practice, it cannot escape the problem of unwanted classical noise, which reduces the quality of the random bits they produce. Therefore, we need to post-process data from a QRNG’s entropy source to improve the statistical quality of the classical output sequence generated from the quantum entropy source. In this work, we implement and compare six extraction primitives: Von Neumann, Multi-level Peres, Toeplitz-hash, Circulant-hash, Trevisan’s construction, and SHA-256 distillation. Using a large classical random bit stream generated by an experimental QRNG, we evaluate these algorithms based on extraction efficiency (η), computational complexity, and seed-entropy requirements. The findings show that although deterministic approaches, such as Multi-level Peres, outperform von Neumann maps, algebraic approaches, especially Circulant extractors, offer higher throughput (η = 0.90) and lower seed consumption by leveraging the cyclicity of the group Zn. The Trevisan extractor provides strong theoretical security with reduced seed growth, but at the cost of higher computational complexity. In contrast, the SHA-256-based method offers fast practical post-processing but provides no information-theoretic entropy guarantees. Statistical validation via autocorrelation and inter-sequence cross-correlation confirms that all evaluated methods successfully decouple hardware-induced dependencies