Postprocessing for quantum random number generators: entropy evaluation and randomness extraction (1207.1473v2)

Abstract: Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.

• The paper introduces a framework using min-entropy and randomness extractors to differentiate quantum randomness from classical noise in quantum random number generators (QRNGs).
• It details methodology for evaluating min-entropy by separating quantum contributions and implements extractors like Toeplitz-hashing and Trevisan's for provably random outputs.
• Experimental implementations showed extractors passing statistical tests, demonstrating effective postprocessing for secure QRNG applications and optimization insights for hardware/software configurations.

Postprocessing for Quantum Random-Number Generators: Entropy Evaluation and Randomness Extraction

The paper "Postprocessing for quantum random-number generators: entropy evaluation and randomness extraction" authored by Xiongfeng Ma et al., presents a comprehensive framework addressing the challenges in differentiating quantum randomness from classical noise in quantum random-number generators (QRNGs). The framework utilizes min-entropy for quantifying quantum randomness and implements randomness extractors, such as Toeplitz-hashing extractor and Trevisan's extractor, to derive provably random outputs.

Quantum mechanics inherently provides a promising foundation for generating truly random numbers through QRNGs. These generators excel in delivering randomness that cannot be deterministically computed, a significant advantage over traditional pseudorandom-number generators, which are algorithmically predictable given sufficient computational resources. However, in practical implementations, QRNG outputs often contain a mix of quantum signals and classical noise, introducing potential vulnerabilities. Classical noise, being potentially controllable by adversaries, mandates a robust method to ensure that the resultant randomness is exclusively derived from the quantum processes.

Main Contributions

The paper makes notable contributions:

1. Entropy Evaluation Framework: It introduces a methodology for evaluating min-entropy, critical for assessing the randomness sources within QRNGs. This process involves separating quantum contributions from classical noise, exemplified through systems discussed in the literature.
2. Randomness Extraction Implementation: Two types of extractors, Toeplitz-hashing and Trevisan's, are implemented to demonstrate the efficacy of converting the raw outputs of QRNGs into almost uniformly random sequences. Notably, Trevisan's extractor provides advantages including security against quantum adversaries and reduced seed length requirements.

The experiments are rooted in previous technical setups where quantum signals typically follow Gaussian distributions. By measuring the variance of the total, quantum, and source signals, the min-entropy content of QRNG outputs can be effectively calculated, guiding subsequent extractor implementations.

Numerical and Statistical Findings

The paper's experimental implementations demonstrated significant results. The Toeplitz-hashing extractor achieved processing speeds of up to 441 kb/s. Although Trevisan's extractor showed lower speeds (0.7 kb/s), primarily due to complexity in the one-bit extractor component, its development underscores new possibilities in scenarios where the economy of random seed bits is prioritized.

The statistical testing of extractor outputs was rigorous, employing established test suites like diehard, NIST, and testu01. Both the Toeplitz-hashing and Trevisan's extractors produced outputs that passed all tests, highlighting the effectiveness of the stated methodologies in generating high-quality random numbers suitable for secure applications.

Implications and Future Directions

This research has several implications. By ensuring that QRNG outputs are information-theoretically random, the methodologies strengthen their application in sensitive fields such as quantum cryptography. Furthermore, the proposed entropy evaluation process provides invaluable insights into optimizing QRNG hardware and software configurations.

Future work might explore enhancing extractor efficiencies and exploring alternatives to one-bit extractors within Trevisan’s framework. The challenge of lowering computation times in real-world implementations remains critical for broader adoption in high-speed applications. Additionally, expanding the model to diverse QRNG architectures could significantly optimize random number generation across quantum technologies. The domain remains fertile for innovations that marry theoretical developments with practical exigencies in secured communication systems.

In conclusion, this paper sets a methodology with significant implications for both the theoretical validation and practical deployment of QRNG technology, cementing its pivotal role in advancing secure random number generation within quantum information science.