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arXiv:1404.5977

An Observed-Data-Consistent Approach to the Assignment of Bit Values in a Quantum Random Number Generator

Pavel Lougovski, Raphael C. Pooser

Published Apr 23, 2014• 1 citation
arXivHTMLPDF

Abstract

The majority of Quantum Random Number Generators (QRNG) are designed as converters of a continuous quantum random variable into a discrete classical random bit value. For the resulting random bit sequence to be minimally biased, the conversion process demands an experimenter to fully characterize the underlying quantum system and implement parameter estimation routines. Here we show that conventional approaches to parameter estimation (such as e.g. {\it Maximum Likelihood Estimation}) used on a finite QRNG data sample without caution may introduce binning bias and lead to overestimation of the randomness of the QRNG output. To bypass these complications, we develop an alternative conversion approach based on the Bayesian statistical inference method. We illustrate our approach using experimental data from a time-of-arrival QRNG and numerically simulated data from a vacuum homodyning QRNG. Side-by-side comparison with the conventional conversion technique shows that our method provides an automatic on-line bias control and naturally bounds the best achievable QRNG bit rate for a given measurement record.

DOI
10.48550/arxiv.1404.5977

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Quantum random number generators (QRNGs) offer a fundamentally different approach to random number generation compared to classical methods, leveraging the inherent randomness of quantum processes. However, their practical implementation and analysis often face challenges, particularly concerning the accurate characterization of the underlying probability distribution and the optimization of generation algorithms. This paper presents a comprehensive probability analysis of QRNG output, focusing on identifying and quantifying sources of bias and uncertainty. We introduce a novel framework combining quantum information theory and statistical analysis to rigorously evaluate QRNG performance. Furthermore, we propose an optimization strategy based on adaptive sampling techniques and error correction, aiming to enhance both the security and efficiency of QRNGs. Our approach provides a detailed understanding of QRNG behavior and offers actionable insights for designing and deploying robust QRNG systems. The core of our analysis lies in the precise determination of the output probability distribution, denoted as P(s1, s2, ..., sK), where K represents the number of bits generated. We demonstrate how this distribution can be refined through iterative statistical estimation and how this information can be used to improve the generation process.
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A quantum random number generator (QRNG) provides a reliable means for the generation of true random numbers. The inherent randomness of the vacuum fluctuations makes the quantum vacuum state a superior source of entropy. However, in practice, the raw sequences of QRNG are inevitably contaminated by classical technical noise, which compromises the security of the QRNG. Min-entropy conditioned on the classical noise is a useful method that can quantify the side-information independent randomness. To improve the extractable randomness from the raw sequences arising from the quantum vacuum-based QRNG, we propose and experimentally demonstrate two approaches, discarding-boundary-bin measurement and multi-interval sampling. The first one increases the conditional min-entropy at a low quantum-to-classical-noise ratio. The latter exploits parallel sampling using multiple analog-to-digital converters (ADCs) and effectively overcomes the finite resolution limit and uniform sampling of a single ADC. The maximum average conditional min-entropy can reach 9.2 per sample when combining these two approaches together in contrast to 6.93 with a single 8-bit ADC.
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Quantum random number generation (QRNG) offers a fundamentally different approach to randomness compared to classical methods. This paper explores the design and principles of a QRNG based on harnessing the inherent uncertainty in quantum measurements. The core claim is the development of a system capable of generating truly random quantum bit sequences. This is achieved by exploiting the probabilistic nature of quantum measurement, specifically the collapse of the wave function upon observation, which yields unpredictable outcomes. The generated sequences are expected to exhibit statistical independence, a crucial property for various quantum computing applications. This work lays the groundwork for a detailed exploration of QRNG techniques, highlighting their potential impact on secure quantum communication and simulation. We will detail the theoretical underpinnings, focusing on the mathematical formulation of the process and the statistical properties of the generated random numbers.
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