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arXiv:1501.02959 · Physical Review A

Strong experimental guarantees in ultrafast quantum random number generation

Morgan W. Mitchell, Carlos Abellán, Waldimar Amaya

Published Jan 12, 2015• 50 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.91.012314

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A quantum random number generator (QRNG) can generate true randomness by exploiting the fundamental indeterminism of quantum mechanics. Most approaches to QRNG employ single-photon detection technologies and are limited in speed. Here, we experimentally demonstrate an ultrafast QRNG at a rate over 6 Gbits/s based on the quantum phase fluctuations of a laser operating near threshold. Moreover, we consider a potential adversary who has partial knowledge on the raw data and discuss how one can rigorously remove such partial knowledge with postprocessing. We quantify the quantum randomness through min-entropy by modeling our system and employ two randomness extractors--Trevisan's extractor and Toeplitz-hashing--to distill the randomness, which is information-theoretically provable. The simplicity and high-speed of our experimental setup show the feasibility of a robust, low-cost, high-speed QRNG.
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 Number Generators (RNGs) are crucial for applications ranging from cryptography to simulations. Depending on the source of randomness, RNGs are classified into Pseudo-Random Number Generators (PRNGs), True Random Number Generators (TRNGs), and Quantum Random Number Generators (QRNGs). This work presents the end-to-end development of a high-speed, high-efficiency, phase-noise-based QRNG system that taps into the quantum phase noise of a single-frequency laser, with randomness originating from spontaneous emission. Using a self-heterodyne measurement with a semiconductor laser (linewidth ≈\approx≈ 5.23 GHzGHzGHz) operated near threshold and a $\sim$48 cmcmcm fiber delay line, a raw data generation rate of 2.0 GbpsGbpsGbps is achieved. To ensure uniform randomness in the QRNG output, robust extraction techniques developed in-house, such as the Toeplitz Strong Extractor (TSE), are used. Randomness validation using the NIST and Diehard test suites confirms that all statistical tests pass at standard confidence levels. The developed system achieves a post-processed generation rate of 1.0 GbpsGbpsGbps in operation and attains a Technology Readiness Level (TRL) of 7, approaching TRL 8, making it suitable for real-time secure applications such as cryptographic key generation and stochastic modeling.
Random numbers are one of the key foundations of cryptography. This work implements a discrete quantum random number generator (QRNG) based on the tunneling effect of electrons in an avalanche photo diode. Without any post-processing and conditioning, this QRNG can output raw sequences at a rate of 100 Mbps. Remarkably, the statistical min-entropy of the 8,000,000 bits sequence reaches 0.9944 bits/bit, and the min-entropy validated by NIST SP 800-90B reaches 0.9872 bits/bit. This metric is currently the highest value we have investigated for QRNG raw sequences. Moreover, this QRNG can continuously and stably output raw sequences with high randomness over extended periods. The system produced a continuous output of 1,174 Gbits raw sequence for a duration of 11,744 s, with every 8 Mbits forming a unit to obtain a statistical min-entropy distribution with an average value of 0.9892 bits/bit. The statistical min-entropy of all data (1,174 Gbits) achieves the value of 0.9951 bits/bit. This QRNG can produce high-quality raw sequences with good randomness and stability. It has the potential to meet the high demand in cryptography for random numbers with high quality.
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.
For quantum random number generators (QRNGs), strong security guarantees can be obtained under various assumptions. The most well-known assumptions are the non-signalling assumption (needed for device-independent (DI) QRNG) and post-quantum computational assumptions (needed for computationally bounded single-prover QRNG protocols). In this work, we study a third model: a simple prepare-and-measure QRNG whose security relies on physically motivated energy constraints. This physically motivated set-up allows for easier implementations of QRNGs and can supply better rates. So far, previous works that studied the energy-constrained model either assumed that the adversary is classical in their security proof or supplied relatively weak bounds on the certified randomness, by bounding the conditional min-entropy. In this work, we prove a new, essentially tight, lower bound on the single-round von Neumann entropy against adversaries holding both classical and quantum side-information. Our work reveals that working with the von Neumann entropy, rather than the min-entropy, in the quantum case can lead to a major improvement, nearly matching the classical bound in many cases. We further study the robustness of our entropy bound. Since the single-round von Neumann entropy is the main quantity of interest when characterizing the key rate of QRNGs, our bound establishes the main ingredient for rigorous security proofs against general quantum attacks in this framework.