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arXiv:2306.11361 · Wave Electronics and its Application in Information and Telecommunication Systems (WECONF)

Digitization of a Random Signal from the Interference of Laser Pulses : Issue of Randomness Extraction for a Quantum Random Number Generator

Roman Shakhovoy

Published May 29, 2023• 1 citation
arXivHTMLPDF

Abstract

In the study of quantum random number generators (QRNGs), the problem of random signal digitization is often not considered in detail. However, in the context of a standalone QRNG device, this issue is very important. In this paper, we consider the problem of digitizing laser pulses with random intensity and analyze various approaches used to estimate the contribution of classical noise. A simple method for determining the quantum reduction factor suitable for digitization with an analog-to-digital converter is proposed.

DOI
10.1109/weconf57201.2023.10147933

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In the study of quantum random number generators (QRNGs), the problem of random signal digitization is often not considered in detail. However, in the context of a standalone QRNG device, this issue is very important. In this paper, we consider the problem of digitizing laser pulses with random intensity and analyze various approaches used to estimate the contribution of classical noise. A simple method for determining the quantum reduction factor suitable for digitization with an analog-to-digital converter is proposed.
Gain-switched lasers are in demand in numerous quantum applications, particularly in systems of quantum key distribution and in various optical quantum random number generators. The reason for this popularity is natural phase randomization between gain-switched laser pulses. The idea of such randomization has become so familiar that most authors use it without regard to the features of the laser operation mode they use. However, at high repetition rates of laser pulses or when pulses are generated at a bias current close to the threshold, the phase randomization condition may be violated. This paper describes theoretical and experimental methods for estimating the degree of phase randomization in a gain-switched laser. We consider in detail different situations of laser pulse interference and show that the interference signal remains quantum in nature even in the presence of classical phase drift in the interferometer provided that the phase diffusion in a laser is efficient enough. Moreover, we formulate the relationship between the previously introduced quantum reduction factor and the leftover hash lemma. Using this relationship, we develop a method to estimate the quantum noise contribution to the interference signal in the presence of phase correlations. Finally, we introduce a simple experimental method based on the analysis of statistical interference fringes, providing more detailed information about the probabilistic properties of laser pulse interference.
We propose a method for quantum noise extraction from the interference of laser pulses with random phase. Our technique is based on the calculation of a parameter, which we called the quantum reduction factor, and which allows for the determination of the contributions of quantum and classical noises with the assumption that classical fluctuations exhibit Gaussian distribution. To the best of our knowledge, the concept of quantum reduction factor is introduced for the first time. We use such an approach to implement the post-processing-free optical quantum random number generator with the random bit generation rate of 2 Gbps.
Randomness is essential ingredient for applications in cryptography, stochastic simulation, and fundamental science experiments [American Scientist 89, 4 (2001); PRL 115, 25 (2015)]. Common practice is to generate random numbers from mathematical algorithm using Pseudo-random number generators. We are interested in tackling this problem with quantum technology. Phase diffusion in spontaneous emission events is a quantum phenomena with inherent randomness [Opt. Express 19, 21 (2011)]. Implementations of this scheme using pulsed lasers can yield high-speed quantum random number generation (QRNG) [Opt. Express 22, 2 (2014)]. The general interest in the laser phase diffusion QRNG setup has been mainly focused on and motivated by the speed of the random number generations. Little has been stated about the performance of quantum phase noise as a randomness source in QRNG, from the perspective of the physics involved. We reanalyze the process of phase diffusion based QRNG and give an intuitive explaining picture of the underlying physics. Our findings show that a pulsed process is beneficial over the continuous-wave approach and give a upper bound of maximum random bit rate for a given experimental setting. In detail, the output of a semiconductor laser contains fluctuations in intensity and phase. This was originally studied first by Charles Henry in 1982 [J. Lightwave Techn. 4, 3 (1986)]. Based on that one can identify two phenomena contributing to the phase noise, which takes the form of a random walk. First, there will be phase changes due to the carrier-induced change in refractive index in the semiconductor laser. Second, spontaneous emission events take place in the active medium [Opt. Express 19, 21 (2011)]. Naturally, taking spontaneous emission events into account necessitates the application of stochastic laser rate equations for theoretical description. We solve these equations numerically be a Monte-Carlo simulation and investigate several random walk scenarios. One of our essential findings is that the phase fluctuation becomes much larger in the pulsed laser regime than in the continuous-wave mode. Additionally, there is a natural limit on the maximum pulse repetition rate for a given pulse width, since the phase jumps become smaller for shorter pulse distances. Since phase measurement is not a feasible procedure for optical signals, the phase fluctuation needs to be converted to an observable macroscopic parameter such as the optical intensity. This can be done by using an interferometer setup. The whole experimental setting is shown in Fig. 2 (left). An DFB laser diode is modulated using gain-switching technique to generate uniform amplitude signals with random phases. Each signal interferes with neighboring pulses through an unbalanced Mach-Zehnder interferometer. The delay in one arm was set to equal to the pulse repetition rate. With this setup we investigate the influence of several parameters on the shape of the probability distribution determining the quality of QRNG. The theoretical as well as experimental findings can help to find physical standards for QRNG verification rather than the ones based on classical statistical information theory.
Randomness is widely used in various fields, including encryption, statistical analysis, and numerical simulations. Randomness is also a fundamental resource in science and engineering. For such applications, we usually need to provide unbiased and independent random bits. This raises the issue of where to get these supposed random bits. Quantum random number generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. In practice, unfortunately, quantum randomness is inevitably mixed with classical randomness due to classical noise. Also, randomness is often correlated and biased. It is necessary to process the resulting raw bits sequence and convert them to good-quality output values that are as close to uniform distribution as possible. Random extractors are required for this. We analyze the randomness obtained by quantum random number generators as well as various examples of post-processing. We discuss the types of randomness extractors. Also, we use information-theoretically secure extractors and present improved novel randomness extraction.
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.
We consider the problem of quantum noise extraction from polarization swapping in a gain-switched VCSEL. The principle of operation of a quantum random number generator is based on the generation of laser pulses with one of two orthogonal polarization states, followed by digitization of polarization-resolved pulses with a comparator. At intensity values of laser pulses close to the threshold value of the comparator, the contribution of the classical noise of the photodetector will have a crucial role in making a decision on the choice of a logical zero or one. We show how to evaluate the contribution of classical noise and how to calculate the quantum reduction factor required for post-processing.