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Physical Review Applied

Characterizing Phase Noise in a Gain-Switched Laser Diode for Quantum Random-Number Generation

V. Lovic, Davide G. Marangon, Marco Lucamarini, Zhiliang L. Yuan, Andrew J. Shields

Published Nov 4, 2021• 37 citations
Publisher

Abstract

While operating a quantum random-number generator (QRNG), it is extremely useful to have a model of the physical entropy source to guarantee that the device is delivering randomness of genuine quantum origin. In this work we consider a QRNG based on a gain-switched laser diode and we develop a model to quantify its phase noise. This model is based on the laser rate equations and the state-of-the-art techniques for the characterization of laser diodes used in lightwave systems. These tools let us achieve a faithful modeling of the phase noise and we verify its accuracy through comparisons with experimental measurements. Furthermore, the model can be used to select optimal parameters to maximize the QRNG performance and monitor the device behavior to detect malfunctioning or malicious tampering of the device.

DOI
10.1103/physrevapplied.16.054012

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While operating a quantum random-number generator (QRNG), it is extremely useful to have a model of the physical entropy source to guarantee that the device is delivering randomness of genuine quantum origin. In this work we consider a QRNG based on a gain-switched laser diode and we develop a model to quantify its phase noise. This model is based on the laser rate equations and the state-of-the-art techniques for the characterization of laser diodes used in lightwave systems. These tools let us achieve a faithful modeling of the phase noise and we verify its accuracy through comparisons with experimental measurements. Furthermore, the model can be used to select optimal parameters to maximize the QRNG performance and monitor the device behavior to detect malfunctioning or malicious tampering of the device.
The quantum phase noise in a pulsed semiconductor laser is studied thoroughly in the context of its utilization as a quantum entropy source in a quantum random number generator (QRNG) device. We performed a numerical analysis of the phase diffusion process for a semiconductor laser in the continuous-wave operation mode and gain-switched (GS) mode. The result demonstrates the amplification of randomness in the GS mode, which is gauged physically by the variance VarΔϕ. The variance value, which is mathematically related to the temporal distance between the laser pulses used in the experimental setup, also determines the stability of the setup. Furthermore, we show how the QRNG probability distribution is influenced by several experimental factors such as the quality of the interference process and the noise in the detection system.
Quantum random number generation (QRNG) has become a topic of growing interest in recent years due to important applications in cryptography and simulations. Interferometric detection of phase diffusion in gain-switched single-mode semiconductor lasers is one of the main generation techniques. In this paper, we study experimentally and theoretically the phase diffusion in gain-switched discrete mode laser diodes. We derive a stochastic rate equations model for the laser electric field that avoids numerical instabilities that appear when simulating amplitude and phase equations. Measurements are performed in order to extract the parameters of our semiconductor laser. Spontaneous emission rate coupled into the lasing mode is measured as a function of the carrier number for bias currents below threshold. A quadratic dependence is obtained that permits us to evaluate the validity of the linear approximations that have been used to describe laser phase diffusion in QRNG. The good agreement between experiments and theory permits us to give a realistic quantitative description of the dynamical evolution of the phase statistics in this type of QRNGs.
Quantum random number generators (QRNGs) based on semiconductor laser phase noise are an inexpensive and efficient resource for true random numbers. Commercially available technology allows for designing QRNG setups tailored to specific use cases. However, it is important to constantly monitor whether the QRNG is performing according to the desired security standards in terms of independence and uniform distribution of the generated numbers. This is especially important in cryptographic applications. This paper presents a test scheme that helps to assess the acceptable operating conditions of a semiconductor laser for QRNG operation, using commonly accessible methods. This can be used for system monitoring, but crucially also to help the user choose the laser diode that better suits their needs. Two specific quality measurements, ensuring proper operation of the device, are explained and discussed. Setup-specific approaches for setting an acceptance boundary for these measures are presented, and exemplary measurement data showing their effectiveness are given. By following the comprehensible procedure described here, a QRNG qualification environment tailored to specific security requirements can be reproduced.
We report a characterization of the polarization fluctuations observed when gain-switching vertical-cavity surface-emitting lasers (VCSELs) for quantum random number generation (QRNG) applications. We compare our experimental measurements with the results obtained from a stochastic rate equations model that incorporates the intrinsic parameters of the VCSEL found using the state-of-the-art experimental techniques. The good agreement obtained between our experiments and simulations can be used to establish a validation process that permits monitoring of the device behavior to detect malicious intrusion or malfunctioning of the QRNG. Simulations of the model are used to look for parameters that maximize the QRNG performance. Along this direction we consider the performance when considering a VCSEL with vanishing values of the amplitude and phase anisotropies. We show that in this system the obtained raw bits have a low bias value that is independent of the sampling time chosen to obtain the random bit and of the parameters of the modulation. We also use the simulations of the model to predict the QRNG performance at high modulation frequencies. We show that random bits obtained at several Gbps rates, after appropriate post-processing, fully pass the NIST statistical test.
The quantum random number generation based on laser phase noise, which is featured with high random number generation rate and ease for photonic integration, has been extensively investigated and demonstrated. Despite these advancements, a theoretical model to achieve optimal performance in terms of maximizing the random number generation rate is still incomplete. In this work, a comprehensive physical model for this scheme is introduced to accurately predict the power spectrum of entropy source and probability distribution of raw data, based on which the entropy source bandwidth and extractable randomness can be accordingly estimated and thus the system performance can be quantitatively evaluated and optimized. The model is sufficiently validated through both simulation and experiment with significant agreement under various typical setups. Furthermore, our proposal enables the proactive design of experimental parameters to achieve optimal system performance, which is crucial for the design and practical implementation of photonics integrated quantum random number generations.