QPP-RNG: A Conceptual Quantum System for True Randomness

Abstract

We propose and experimentally demonstrate the \emph{Quasi-Superposition Quantum-inspired System (QSQS)} -- a conceptual quantum system for randomness generation built on measuring two conjugate observables of a permutation sorting process: the deterministic permutation count $n_p$ and the fundamentally non-deterministic sorting time $t$. By analogy with quantum systems, these observables are linked by an uncertainty-like constraint: algorithmic determinism ensures structural uniformity, while system-level fluctuations introduce irreducible unpredictability. We realize this framework concretely as \emph{QPP-RNG}, a system-embedded, software-based true random number generator (TRNG). In QPP-RNG, real-time measurements of sorting time $t$ -- shaped by CPU pipeline jitter, cache latency, and OS scheduling -- dynamically reseed the PRNG driving the permutation sequence. Crucially, QSQS transforms initially right-skewed raw distributions of $n_p$ and $t$ into nearly uniform outputs after modulo reduction, thanks to internal degeneracies that collapse many distinct states into the same output symbol. Empirical results show that as the repetition factor $m$ increases, output entropy converges toward theoretical maxima: Shannon and min-entropy values approach 8 bits, chi-squared statistics stabilize near ideal uniformity, and bell curves visually confirm the flattening from skewed to uniform distributions. Beyond practical implications, QSQS unifies deterministic algorithmic processes with non-deterministic physical fluctuations, offering a physics-based perspective for engineering true randomness in post-quantum cryptographic systems.