Experimental study of a quantum random-number generator based on two independent lasers

A quantum random-number generator (QRNG) can produce true randomness by utilizing the inherent probabilistic nature of quantum mechanics. Recently, the spontaneous-emission quantum phase noise of the laser has been widely deployed for quantum random-number generation, due to its high rate, its low cost, and the feasibility of chip-scale integration. Here, we perform a comprehensive experimental study of a phase-noise-based QRNG with two independent lasers, each of which operates in either continuous-wave (CW) or pulsed mode. We implement the QRNG by operating the two lasers in three configurations, namely, CW + CW, CW + pulsed, and pulsed + pulsed, and demonstrate their trade-offs, strengths, and weaknesses.

Figure 1

Experimental setup for the QRNG. Two independent lasers (LD1 and LD2) interfere at a beam splitter (BS) whose output is detected by a photodetector (PD) followed by an oscilloscope. The output voltage of the photodetector is ac-coupled to the oscilloscope, whose sampling rate is determined by the configuration (see the text). Each analog sample is converted to 8 digital bits by an 8-bit analog-to-digital converter.

Figure 2

Measured output voltage (left) and probability density function (right) for electrical (e) noise (dashed black curve) and total phase noise, CW + CW (solid red curve), CW + pulsed (dashed green curve), and pulsed + pulsed (dash-dotted blue curve). The classical noise includes the classical phase noise coming from the interferometer, the intensity fluctuation noise of the two lasers, and the classical electrical noise of the photodetector and oscilloscope. But as in the analysis in the Appendix, the classical phase noise of the interferometer is ignored here, and a detailed figure of the second and third classical noises is given in the Appendix (Fig. 4). In all measurements, the sampling rate of the oscilloscope is 20 GHz, and the recorded sample size is ${10}^8$. The maximal amplitudes of phase noises are 82.9, 70.8, and 65.7 mV for CW + CW, CW + pulsed, and pulsed + pulsed, respectively.

Figure 3

(a) The Autocorrelation coefficient of raw data (dotted curves) and extracted data (solid curves) for case I (red stars), case II (blue circles), and case III (green squares). The autocorrelation coefficient is calculated with the length of data ${10}^8$ and statistical significance $\alpha =0.01$. And the calculated $P$ values of the autocorrelation coefficients are given in Fig. 6 (Appendix); all of them are larger than $\alpha =0.01$. In order to show the autocorrelation coefficient clearly, the absolute value $\left|R\right(k\left)\right|$ is plotted. The autocorrelation coefficient of extracted data is rather low (normally below 0.001), which means a high-quality random number is obtained after postprocessing. (b) NIST test results for 1 Gbit of extracted data in each case. Labels on the $X$ axis represent the 15 NIST test terms. For each test term, the bar values from left to right represent the $P$ values for the three cases [30]. The extracted data successfully pass all NIST tests in all three cases.

Figure 4

Measurement results for the CW + CW case. (a) Beating signal's frequency. The sampling rate is 10 GHz in this measurement. The solid line is the Gaussian fitting curve for the experimental data. The beating signal has mean 278.7 MHz and standard deviation 30.2 MHz. (b) Autocorrelation coefficient of the PD's output at sampling frequencies of 100 MHz (solid blue curve), 50 MHz (dashed red curve), and 20 MHz (dash-dotted yellow curve).

Figure 5

Observed probability density function (PDF) of the classical noise: electrical noise (red dots), intensity noise of LD1 (green circles), and intensity noise of LD2 (blue $\mathsf{x}$'s). The experimental setups are the same as those in the text. But we turn off the two lasers for measurement of the electrical noise and one of the lasers for measurement of the intensity noise of LD1 and LD2. The sampling rate of the oscilloscope is 20 GHz, and the recorded sample size is ${10}^8$.

Figure 6

$P$ value for the autocorrelation coefficient of the extracted bit string. In the calculation, the length of the data is ${10}^8$, and the statistical significance is set at $\alpha =0.01$. All of them are larger than the statistical significance, which means that there is insufficient evidence to conclude that there is a significant relationship between the bit string $X=\left[x_i\right]$ and $X^{\prime }=\left[x_{i+k}\right]$.