Security Evaluation of Laser-Phase-Noise Quantum Random Number Generators with Intrinsic Correlations

Quantum random number generators (QRNGs) based on laser phase noise are popular for their simplicity and integration potential. However, these systems often face a trade-off: to ensure high-quality, independent random numbers, the optical delay line must be significantly longer than the laser's coherence time. As researchers push for more compact, chip-scale devices, shorter delay times are used, which inevitably introduce intrinsic temporal correlations into the raw data. This paper addresses the critical need for a rigorous security evaluation framework that accounts for these correlations, rather than relying on the standard independent and identically distributed (i.i.d.) assumption.

The researchers establish a theoretical model for single-laser phase noise schemes, treating the laser phase as a Wiener process. They derive an analytical expression for the correlation coefficients of the raw data based on the temporal overlap of phase evolution intervals. To quantify the actual extractable randomness, they formulate a conditional min-entropy expression that incorporates both these intrinsic correlations and classical electronic noise. The model is validated through numerical simulations across various physical regimes, comparing theoretical predictions with autocorrelation coefficients calculated from large-scale simulated datasets.

The study demonstrates that the proposed analytical model accurately characterizes the system's correlation properties across different operating conditions. A key finding is that in typical experimental setups, failing to account for intrinsic correlations results in a 46% overestimation of the extractable secure randomness. By providing a tractable analytical expression for conditional min-entropy, the authors offer a practical tool for designers to optimize the trade-off between device miniaturization and the rigorous security requirements of cryptographic systems.