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A Simple Five-Bit Quantum Random Digit Generator

Eric Thompson

Published May 7, 2026• 0 citations
Publisher

Abstract

Quantum random number generators provide physical randomness by converting intrinsically probabilistic measurement outcomes into usable digital values. This white paper presents a simple five-bit protocol for generating uniformly distributed decimal digits from an ideal 50/50 quantum source. Five independent binary outcomes produce 2⁵ = 32 possible sequences. By rejecting the two extreme runs, 00000 and 11111, exactly 30 admissible sequences remain, allowing a direct uniform mapping onto the ten decimal digits.The main contribution of this note is not entropy-optimal extraction, but transparency: the protocol is easy to inspect, easy to implement, and easy to explain to nontechnical users. This makes it especially relevant for trust-critical public-facing applications where visible fairness may matter more than maximum entropy efficiency. A small efficiency improvement is also introduced. Instead of discarding a rejected extreme run entirely, the rejected all-A or all-B sequence is recycled as a single fair starting bit for the next five-bit candidate block. Under the assumption of independent fair input bits, this carry-forward rule preserves exact decimal uniformity while improving the expected raw-bit cost from 16/3 ≈ 5.333 bits per digit to 79/15 ≈ 5.267 bits per digit.The paper also discusses practical implementation using a beam-splitter-style quantum randomness source, limitations under detector imbalance, and the proper cryptographic positioning of the method. The protocol can serve as a transparent entropy source or educational QRNG digitization scheme, but cryptographic deployment would still require standard health testing, calibration, and extraction.

DOI
10.5281/zenodo.20076445

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Quantum random number generators provide physical randomness by converting intrinsically probabilistic measurement outcomes into usable digital values. This white paper presents a simple five-bit protocol for generating uniformly distributed decimal digits from an ideal 50/50 quantum source. Five independent binary outcomes produce 2⁵ = 32 possible sequences. By rejecting the two extreme runs, 00000 and 11111, exactly 30 admissible sequences remain, allowing a direct uniform mapping onto the ten decimal digits.The main contribution of this note is not entropy-optimal extraction, but transparency: the protocol is easy to inspect, easy to implement, and easy to explain to nontechnical users. This makes it especially relevant for trust-critical public-facing applications where visible fairness may matter more than maximum entropy efficiency. A small efficiency improvement is also introduced. Instead of discarding a rejected extreme run entirely, the rejected all-A or all-B sequence is recycled as a single fair starting bit for the next five-bit candidate block. Under the assumption of independent fair input bits, this carry-forward rule preserves exact decimal uniformity while improving the expected raw-bit cost from 16/3 ≈ 5.333 bits per digit to 79/15 ≈ 5.267 bits per digit.The paper also discusses practical implementation using a beam-splitter-style quantum randomness source, limitations under detector imbalance, and the proper cryptographic positioning of the method. The protocol can serve as a transparent entropy source or educational QRNG digitization scheme, but cryptographic deployment would still require standard health testing, calibration, and extraction.
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.
Random numbers play a significant role in fields like scientific simulations and cryptography. Here we describe a physical random number generator based on the intrinsic randomness of quantum mechanics. We design a simple method to produce and analyze random sequences starting with a source of correlated/entangled photon pairs as an entropy source. We generate random bits from the coincidence rates of photon pairs in 3 steps: (i) generate correlated/entangled photon pairs, (ii) convert the coincidence rates from decimal to binary, (iii) apply a randomness extraction procedure (post-processing). In this approach, we have tested the influence of entanglement on the entire generation process. In order to obtain a good-quality random sequance, we have used and compared two different extractors in the post-processing step.
In this thesis we study the generation of randomness from quantum mechanical sources: quantum random number generators (QRNGs). Such devices are thought to provide a better quality of randomness than is possible with classical devices, but the issue is in need of more rigorous study. In Chapter 1 we provide the necessary background for the thesis from both computability and probability theory. We then present and extend some recent results providing a more theoretical grounding for the indeterminism in quantum mechanics. In particular, we show that sequences of quantum random bits are incomputable in the strongest sense: no bit can be provably computed in advance. In Chapter 2 we study in detail the use of von Neumann normalisation for QRNGs producing both finite strings and infinite sequences of bits; such normalisation methods are necessary in order to counter for experimental imperfections. We show that, in the case of a constantly biased source, this normalisation gives the desired uniform distribution. The effect of this normalisation on the (in)computability of the generated sequences is studied, and it is shown that algorithmic randomness and Borel normality are preserved, but e-randomness (and thus incomputability) is, in general, not. Experimental bounds for the extent of departure from the uniform distribution in the non-ideal case of a slowly drifting bias are derived. In Chapter 3 we propose a new QRNG which uses entangled photon pairs and is certified to produce incomputable bits by value indefiniteness; this is the first QRNG with explicit certification by a physical principle. The effects of various experimental imperfections are discussed in detail, and care is taken to make the proposed QRNG as robust as is possible to these. A robust method based on XORing the produced bitstrings together is proposed to further improve the quality of the distribution produced by the QRNG. Various improvements and optimisations to this scheme are discussed.
Quantum random number generators (QRNG) are the prime source of randomness, by exploiting the unpredictable nature of Quantum mechanics QRNG aims to provide a string of completely random utterly unpredictable numbers. QRNGs are crucial for cryptography, scientific calculation, simulation, and many more real-world applications. Our Optical Quantum Random Number Generator (OQRNG) utilizes a high-speed pulsating laser, a Polarizing beam splitter (PBS), photodetectors, and advanced signal processing units that capture and digitize random photon intensity forming the raw random bit stream. This technique is famously known as Branching Path Technique. After that, we implement rigorous testing that encompasses the statistical randomness tests developed by National Institute of Standards and Technology (NIST) to ensure the guaranteed ran-domness meets security standards. A user-friendly Graphic user interface (GUI) simplifies interaction with the QRNG allowing the user to configure device settings, monitor system performance, and securely extract random numbers. Our findings help us demonstrate the superiority of QRNGs over classical random number generators, and highlight the potential of photon-based QRNGs and their environmentally friendly and efficient random number generation.
We describe a methodology and standard of proof for experimental claims of quantum random-number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations, lower bounds on the quantum contribution to the average min-entropy can be derived from measurements on the QRNG output. Given these bounds, randomness extractors allow generation of nearly perfect ``$\ensuremath{\epsilon}$-random'' bit streams. An analysis of experimental uncertainties then gives experimentally derived confidence levels on the $\ensuremath{\epsilon}$ randomness of these sequences. We demonstrate the methodology by application to phase-diffusion QRNG, driven by spontaneous emission as a trusted randomness source. All other factors, including classical phase noise, amplitude fluctuations, digitization errors, and correlations due to finite detection bandwidth, are treated with paranoid caution, i.e., assuming the worst possible behaviors consistent with observations. A data-constrained numerical optimization of the distribution of untrusted parameters is used to lower bound the average min-entropy. Under this paranoid analysis, the QRNG remains efficient, generating at least 2.3 quantum random bits per symbol with 8-bit digitization and at least 0.83 quantum random bits per symbol with binary digitization at a confidence level of 0.999 93. The result demonstrates ultrafast QRNG with strong experimental guarantees.
Random numbers generated via quantum process is indeterministic, which are of essential to the cryptographic communication and the large-scale computer modeling. However, in realistic scenarios, classical noises can inevitably contaminate the raw sequences of a quantum randomness number generator (QRNG), and then compromise the security of the QRNG. Min-entropy is a useful approach that can quantify the randomness independent of side-information. To enhance the extractable randomness of the raw sequences arising from the QRNG, we propose a new method which exploits non-uniform quantization methods instead of uniform sampling methods and effectively enhances the extractable randomness from the QRNG at a high quantum-to-classical-noise ratio (QCNR). Given a QCNR as 50 dB and a 16-bit analog-to-digital converter (ADC), the worst-case conditional min-entropy of the non-uniform quantization scheme is improved by nearly 11% compared with that of the uniform sampling scheme.