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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Quantum random numbers based on the vacuum state

C. Gabriel, Christoffer Wittmann, Сыч Денис Васильевич, Ruifang Dong, Wolfgang Mauerer, Ulrik L. Andersen, Christoph Marquardt, Gerd Leuchs

Published May 1, 2011• 0 citations
Publisher

Abstract

We present a generator producing unique and truly random bit sequences based on the measurement of the quantum uncertainty of a continuous variable vacuum state. Vacuum states have the advantage of being inherently pure states, i.e. they cannot be tempered with by an adversary and are easily detectable. Therefore, they are an ideal resource for a quantum RNG. Our RNG consists of a simple homodyne detection system.

DOI
10.1109/cleoe.2011.5943457

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We present a generator producing unique and truly random bit sequences based on the measurement of the quantum uncertainty of a continuous variable vacuum state. Vacuum states have the advantage of being inherently pure states, i.e. they cannot be tempered with by an adversary and are easily detectable. Therefore, they are an ideal resource for a quantum RNG. Our RNG consists of a simple homodyne detection system.
Information-theoretically provable unique true random numbers, which cannot be correlated or controlled by an attacker, can be generated based on quantum measurement of vacuum state and universal-hashing randomness extraction. Quantum entropy in the measurements decides the quality and security of the random number generator (RNG). At the same time, it directly determines the extraction ratio of true randomness from the raw data, in other words, it obviously affects quantum random bits generating rate. In this work, we commit to enhancing quantum entropy content in the vacuum noise based quantum RNG. We have taken into account main factors in this proposal to establish the theoretical model of quantum entropy content, including the effects of classical noise, the optimum dynamical analog-digital convertor (ADC) range, the local gain and the electronic gain of the homodyne system. We demonstrate that by amplifying the vacuum quantum noise, abundant quantum entropy is extractable in the step of post-processing even classical noise excursion, which may be deliberately induced by an eavesdropper, is large. Based on the discussion and the fact that the bandwidth of quantum vacuum noise is infinite, we propose large dynamical range and moderate TIA gain to pursue higher local oscillator (LO) amplification of vacuum quadrature and broader detection bandwidth in homodyne system. High true randomness extraction ratio together with high sampling rate is attainable. Experimentally, an extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the laser power of the LO when classical noise excursions of the raw data is obvious.
Summary form only given. The availability of fast and good quality random numbers is necessary to deploy quantum key distribution devices. The state of the universe according to classical mechanics is perfectly determined via its initial conditions. However, in quantum mechanics, the Heisenberg uncertainty relation provides a source of randomness. We present an experiment that taps to this source to provide a fast and reliable stream of random bits.Our experiment setup involves performing a continuous variable homodyne detection of the quantum vacuum state [1]. A 1550 nm fibre coupled laser is split at a 50/50 beam splitter whose outputs are optically coupled to two identical high-speed photo detectors whose photocurrent difference provides a source of entropy. Using methods from classical information theory based on secure hashing functions, the entropy contributions from classical sources, like the electronic dark noise, are characterised and removed from the final generated bits (fig1). This ensures that the randomness in the final bits is solely driven by the quantum fluctuations. The entropy and randomness of the bits generated are being periodically tested using various standard statistical tests on randomness (fig 2). Each test returns a p-value. For a random sequence of numbers, the distributions of the p-values are expected to be uniform.The setup is reliable and robust. To date, it has been continuously generating random bits for more than months at a constant rate of 5.7 Gbits/s. The quantum random numbers are available online [2] via a secure and convenient connection. So far, we have received more than 190000 visits from all over the world served over 40 Gigabytes of random numbers. Each client connection is served with a fresh set of bits.
Quantum random number generators represent one of the most promising techniques for producing truly and unique random numbers, essential in many applications such as quantum communication and cryptography protocols. In this work, we report an experimental implementation of vacuum-based quantum random number generator. By measuring the quantum fluctuations of the radiation ground state, a mixture of a perfectly Gaussian distributed random signal—originating from the intrinsic randomness in the quantum measurement— and an undesired classical electronic noise is obtained. Using an adequate post-processing, the undesired classical contribution of the electronic noise is removed to produce final, quasi-uniformly distributed random bit sequences. The high-quality character of the generated random bits is confirmed by applying the statistical tests of the NIST SP 800-22 test battery.
This paper presents the design and theoretical framework for a quantum random number generator (QRNG) rooted in the principles of quantum mechanics. The core innovation lies in leveraging the inherent randomness associated with quantum measurement, specifically the uncertainty principle, to generate truly random numbers, a significant departure from the limitations of classical random number generators. The proposed system utilizes a measurement process involving a quantum system, such as a photon polarization or a quantum bit, to produce a sequence of random bits. The generated bits are then processed to eliminate bias and ensure high uniformity. The theoretical analysis focuses on quantifying the randomness inherent in the measurement process and demonstrating the potential for generating high-quality random numbers. This work addresses the growing demand for secure communication, cryptography, and simulation applications that require truly random numbers, offering a fundamentally different approach compared to traditional methods.
The quantum random number generation exploits inherent randomness of quantum mechanical processes and measurements. The real-time generation rate of quantum random numbers is usually limited by electronic bandwidth and data processing rates. Here we use a multiplexing scheme to create a fast real-time quantum random number generator based on continuous variable vacuum fluctuations. Multiple sideband frequency modes of a quantum vacuum state within a homodyne detection bandwidth are concurrently extracted as the randomness source. Parallel postprocessing of raw data from three subentropy sources is realized in one field-programmable gate array (FPGA) based on Toeplitz-hashing extractors. A cumulative generation rate of 8.25 Gbps in real time is achieved. The system relies on optoelectronic components and circuits that could be integrated in a compact, economical package.