A Simple Method of Evaluating Laser Diode Suitability for Phase-Noise Based QRNG

TL;DR

The paper tackles the challenge of selecting and monitoring lasers for phase-noise-based QRNGs, ensuring IID outcomes and a near-uniform underlying phase. It proposes a simple qualification framework based on two quantitative criteria—statistical distance to an arcsine distribution and first-lag autocorrelation—plus boundary-determination via simulations accounting for ADC range and noise. The authors validate the approach experimentally on three laser models, mapping their acceptable operating windows and showing that proper boundaries can separate QRNG-eligible from non-eligible conditions. The framework offers a practical tool for designers to select lasers and tailor QRNG operation to security requirements, while noting that full security demands more comprehensive entropy analysis beyond the present two-criterion test.

Abstract

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 which 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 is given. By following the comprehensible procedure described here, a QRNG qualification environment tailored to specific security requirements can be reproduced.

Figures (11)

• Figure 1: Experimental QRNG setup and methods used in this paper. A semiconductor laser is operated in Gain Switching mode with the help of an arbitrary waveform generator (AWG). The driving current $I(t)$ and chip temperature could be varied. The generated laser pulses show phase randomization indicated by the various colors under the pulse envelopes. The pulse train interferes with a delayed version of itself in an asymmetric Mach-Zehnder-Interferometer (aMZI), resulting in pulses of randomized intensity. These are measured with a photodiode (PD) and an oscilloscope. The intensities extracted from these pulses are scrutinized in terms of their statistical properties with Criterion 1, the normalized statistical distance giving the difference of the measured intensity distribution (blue) with respect to an ideal arcsine (black). Criterion 2 is the autocorrelation of the raw pulse train and indicates how similar the pulse train is to a shifted version of itself, shown with gray dashed lines. Ideally, the autocorrelation drops already for low shifts (black curve). If both criteria are fulfilled, the built QRNG setup is assumed to produce true random numbers.
• Figure 2: (a) A Gaussian distribution of the relative phase between two subsequent laser pulses evolves through phase diffusion. Projected to the phase space relevant for interference, it gives a uniform distribution after some time. (b) A recorded pulse intensity histogram and a fitted ideal arcsine distribution resulting from perfect phase randomization. (c) Electrical and optical pulse trace detail recorded with the described setup. The automatically extracted intensity values are marked with red dots and contribute to the intensity distribution above.
• Figure 3: Simulated statistical distance for varying ADC dynamic range fractions taken by the recorded intensity values and varying intensity noise in the system in percent of the ADC range. There is monotonous dependence of the statistical distance with respect to both quantities. The mean $d_{stat}~=~0.155$ serves as the boundary.
• Figure 4: Simulated Statistical distance and its standard deviation at a fixed noise value of 1.5% and an assumed ADC dynamic range fraction of 50%. With increasing sample size, both values decrease and converge. This emphasizes that simulations have to match the experimental conditions.
• Figure 5: Measured autocorrelation coefficients $C_i$ and deviations under QRNG and non-gain-switching conditions. Both datasets were recorded with Laser 3. In QRNG operation, the coefficients are below the boundary and do not decrease with increasing index $i$. Under non-gain-switching conditions, the means decrease at higher indices.