40 Gb/s quantum random number generation based on optically sampled amplified spontaneous emission

We present a photonic approach for fast quantum random number generation based on optically sampled amplified spontaneous emission (ASE). This approach utilizes a terahertz optical asymmetric demultiplexer to sample the ASE and then digitize the sampled optical pulses into random bits using a multi-bit parallel comparator. A proof-of-concept experiment demonstrates that 40 Gb/s random bits with verified randomness can be obtained using our method. The current generation rate is mainly limited by the bandwidth of the available ASE source.


I. INTRODUCTION
True random numbers play crucial roles in various areas, especially for high-tech communication security. Quantum random number generators (QRNGs), extracting the intrinsic randomness from the nondeterministic nature of quantum physics, can provide truly unpredictable and irreproducible random numbers. 1,2 Owing to such an unique advantage, various quantum entropy sources (QESs) have been proposed and utilized to develop QRNGs, including measuring laser phase fluctuations, [3][4][5] photon events, [6][7][8][9][10][11] quantum vacuum fluctuations, 12,13 and the amplified spontaneous emission (ASE). [14][15][16][17][18][19][20] Among them, the ASE-based QRNGs have attracted tremendous attention due to their advantages in achieving high generation rates. For instance, Williams et al. pioneered the work of fast random number generations based on the filtered ASE from a fiber amplifier and produced a 12.5 Gb/s random bit sequence using threshold comparison and off-line XOR decorrelation techniques in 2010. 14 In 2014, our group exploited a similar threshold comparison technique by merging an electrical single-bit analog-to-digital converter (ADC) and a XOR gate and successfully achieved a 2.5 Gb/s realtime QRNG utilizing the filtered ASE from a super-luminescent diode (SLD). 15 In 2017, Wei et al. realized a 1.2 Gb/s real-time generation rate using an electrical multi-bit ADC to digitalize the ARTICLE scitation.org/journal/app ASE from a super-luminescent light emitting diode (SLED). 16 More recently, a continuous-variable random-number generator using the ASE from an Er-doped fiber successfully achieved a maximum generation rate of 2.5 Gb/s. 17 For faster bits rate, some excellent schemes using electrical ADCs and extensive post-processes have been demonstrated. [18][19][20] The latest research indicates that the generation rate could be enhanced to several tens of Gb/s, even on the order of sub-Tb/s. For instance, Li et al. implemented two parallel channels of random bit generation (10 Gb/s in per channel) utilizing spectrally sliced ASE from a single SLD. 18 Wei et al. realized a 280 Gb/s QRNG using a digital logic method to extract 8 bits from each sample at the sampling rate of 40 GSa/s. 19 Argyris et al. reported a 560 Gb/s QRNG by means of a multi-bit representation form to digitize the sampled ASE. 20 However, it should be noted that these ultrafast QRNGs based on electrical single-bit or multi-bit ADCs and advanced data postprocessing methods are merely implemented in theory through off-line extraction from experimental temporal waveforms of the ASE and thus are not truly real-time outputs. Up until now, to the best of our knowledge, 2.5 Gb/s remains the fastest real-time rate realized by all the ASE-based QRNGs with verified randomness. This is far from what is desirable for practical applications because current communication rates have reached 40 Gb/s or even higher.
One of the ultimate hindrances in the actual implementation of the QRNGs with faster real-time bit rate is the timing jitter of electrical ADCs driven by electronic sampling clocks from radio frequency (RF) oscillators. This is because the current RF oscillators inevitably have a large timing jitter and will introduce serious sampling errors between ideal sampling points and real sampling points. 21,22 Up until now, the state-of-the-art electronic clocks deliver at the level of 100 fs of rms jitter even in the 100 MHz low frequency range, which will rapidly deteriorate with the enhancement of operation frequencies and is increasingly difficult to reduce the jitter. Moreover, the severer the electronic jitter is, the larger the sampling deviation and thus the more serious the signal distortion. 22,23 Especially, when the sampling rate is high in the range of 10 GHz, even a small timing jitter can destroy the output code waveform and its associated eye diagram from the electrical ADC. Seriously, this may cause that the quantized waveform cannot be coded correctly into binary random bit sequences. In addition, it is rather difficult to further reduce this electronic jitter. Expectations for further electrical ADCs suggest that it will take at least a decade to improve the electronic jitter performance by an order of magnitude. 24 In consequence, the practical physical bandwidth of high-speed electrical ADCs is commonly limited to few GHz.
Using optical sampling can overcome this limitation caused by the electronic timing error. [23][24][25] This is because when optical pulses with an ultralow jitter at the level of femtosecond (fs) generated by a mode-locked laser (MLL) are used as the sampling clock, 3-4 orders of magnitude lower in jitter can be reduced than that of the traditional electrical clock. Just the reduction of the timing jitter brings that the effective quantization resolution [(i.e., effective number of bits (ENOB)] and the available input analog signal bandwidth can be greatly enhanced. 24 Quantitatively, it can also be seen from Ref. 24 that when the jitter is reduced to the level of 10 fs, the effective quantization resolution and the analog bandwidth at least has the potential to be enhanced to the level of 8 bits and 10 GHz, respectively.
This inspires us to propose and experimentally demonstrate a photonics-based scheme for fast multi-bit quantum random number generation. Specifically, the sampling of the output ASE from a SLD is first done in the optical domain through a terahertz optical asymmetric demultiplexer (TOAD)-based optical sampler. Then, the optically sampled pulses are converted continuously into random bit streams in binary format by an 8-bit parallel comparator built-in a high-speed real-time serial data analyzer. Finally, retention of four least significant bits (LSBs) is implemented at 10 GSa/s sampling rate, and thus, 40 Gb/s (=10 GSa/s × 4 bits) random bit sequences can be successfully extracted.
To the best of our knowledge, this proposal is the first combination of the ASE signals and a photonic sampled ADC. In comparison with the previous QRNG schemes, there exist at least two significant advantages to our approach. (i) Using an optical sampler driven by ultrashort mode-locked optical pulses can overcome the electronic jitter issue confronted by electrical ADCs. This is because the current timing jitter of the MLL is now about 10 fs or even lower. 24 Under this condition, the ASE noise can be optically sampled with higher rate and accuracy. 26,27 (ii) Compared with an 8-bit ADC, the 8-bit parallel comparator in our method does not contain the S/H circuit in its front end. Thus, the 8-bit parallel comparator does not make the function of sampling but only quantize the sampled random pulses from the TOAD with an ultralow timing jitter into binary bit sequences. In this way, the timing jitter issue confronted by the electrical ADC can be solved efficiently.
Moreover, the QRNG rate with our scheme is jointly determined by the number of retained LSBs and the optical sampling rate. In this proof-of-principle experiment, the optical sampling rate is only set at 10 GSa/s controlled by the pulse-repetition rate of the MLL used. Considering the ultrafast response rate of the TOADbased optical sampler, our QRNG is expected to achieve a real-time bit rate up to tens or even hundreds of Gb/s when the bandwidth of the available ASE signals is sufficiently broad. We believe that this work will motivate more implementation of ultrafast QRNGs with associated all-optical signal processing technologies in the near future. Figure 1 is the experimental schematic for implementing the proposed fast QRNG based on the optically sampled ASE noise emitted from a SLD. The whole setup mainly consists of three crucial components: (a) ASE source, (b) optical sampler, and (c) 8-bit parallel comparator, as depicted in Fig. 1. The 8-bit parallel comparator used in experiments is provided by a 36 GHz real-time serial data analyzer (Lecroy, LabMaster10-36Zi, 80 GSa/s sampling rate, 8-bit vertical resolution). Note that the external trigger clock applied in our system is a high-level DC signal so that the sampling function will not be executed during our quantization process. In this way, the real-time serial data analyzer can be used as an 8-bit comparator. In addition, we want to point that utilizing discrete ADC devices (such as AAD08S010G from AcelaMicro and AD9213 from ADI) can also realize the function of a multi-bit comparator as long as the trigger clock is replaced by a high-level DC signal source.

A. ASE source
In our experiments, we selected the ASE noise from the SLD (Thorlabs, SLD1005S) with a 3-dB optical spectrum width of more than 50 nm centered at 1550 nm as the random entropy source. The laser was operated by applying a constant 360.0 mA current (∼4.0 times the laser threshold), while its working temperature was maintained at 24 ○ C with variations less than 0.1 ○ C. In such a case, the output power of the SLD is about 13 mW. First, the ASE noise is filtered by an optical bandpass filter (BPF) working at a center wavelength of 1553.7 nm with a 3-dB bandwidth of 0.6 nm. Then, an EDFA (Keopsys, CEFA-C-HB-CPB30) after the BPF is used to adjust the power of the ASE signal and make it efficiently injected into the optical sampling device (TOAD).
From Fig. 2(a), we can observe that the optical spectrum of the SLD is wide enough to be spectrally demultiplexed into many statistically independent quantum noise sources. Figure 2

ARTICLE
scitation.org/journal/app that the RF spectrum of the filtered ASE is very flat over a wide bandwidth range, which is about 11.8 GHz calculated utilizing the 3-dB bandwidth definition. This kind of high bandwidth level is highly beneficial for subsequent ultrafast random bit extraction. Furthermore, the characteristic of the amplitude distribution of the filtered ASE and the classical noise temporal waveforms are explored. As depicted in Fig. 2(c), the plots labeled "SLD on" show total noises (i.e., the quantum noise and the classical noise) and the plots labeled "SLD off" show the case where only classical noises are contained (i.e., noise sources are mainly contributed from background detections and electronic noises, such as the EDFA, the SOA, the photodetector, and the parallel comparator). Their corresponding probability distributions are also shown in the right side in Fig. 2(c) in which the red line is the Gaussian fitted curve of the obtained total noise amplitude. From the statistical results, one can observe clearly that its amplitude exhibits a Gaussian-like distribution. Such a characteristic is strongly suggestive of enabling the production of un-biased and high-quality random bits. Finally, the signal autocorrelation trace of the filtered ASE temporal waveforms is plotted in Fig. 2(d) with a sample size of 1.6 Mbits. Obviously, there is no dominant correlation peak. This positive feature is mainly due to the fact that the ASE signals are essentially a fundamental quantum phenomenon. In our experiments, the optical spectra are measured by an optical spectrum analyzer with a resolution of 0.02 nm (YOKO-GAWA, AQ6370C). The temporal waveform and the electric power spectrum are detected by a 36 GHz real-time digital oscilloscope (LabMaster10-36Zi, 80 GS/s sampling rate) and a 26.5 GHz radiofrequency spectrum analyzer (Agilent N9020A, 3 MHz RBW, 3 kHz VBW) via a 45 GHz PD (U 2 T, XPDV2120RA). In practice, even though the measured quantum signal (the source of genuine randomness) in the coherent detection-based QRNGs is inevitably mixed with classical noise, 28,29 the genuine randomness still can be extracted from the mixture of quantum signal and classical noise. The premise in terms of satisfying the extraction requirement of signal randomness is not very difficult. When the signal intensity is sufficiently larger than the classical noise, then the contribution of the latter can be neglected. 4,[30][31][32][33] Based on this fact, the method of using a key parameter, quantum-classical noise ratio (QCNR), has been widely adopted to quantify the amount of quantum noise to the amount of classical noise. In this regard, we can describe the variance of the whole system output voltage from the detector as σ 2 t = σ 2 q + σ 2 c, as shown in Fig. 2(c), where σ 2 q and σ 2 c are measured variances of the ASE noise and the classical noise, respectively. The calculated results show that the total measured intensity noise σ 2 t is 225 mV 2 and σ 2 c is 0.81 mV 2 , which is mainly derived from the electronic noise of the detector and quantizer. Furthermore, the quantum variance is obtained as σ 2 q = 224.19 mV 2 . Then, the QCNR [QCNR = 10 log 10 (σ 2 q/σ 2 c)] is achieved at a fixed laser power, and the corresponding QCNR is about 23.8 dB. In other words, the measured quantum signal produced by the SLD is more than 23.8 dB higher than the classical noise. In this case, the corresponding maximum ratio γ (γ = 1 − σ 2 c/σ 2 t ) of the ASE noise to the total noise is 99.64%. [30][31][32][33] These statistical results indicate that the ASE noise is dominant in our system, which guarantees the security and quality of the exacted quantum random bits.

B. Optical sampler
In the sampling part [ Fig. 1(b)], a simple TOAD-based optical sampler is introduced in our proof-of-principle experiment.
The TOAD is an all-optical switch based on the Sagnac interferometer principle. It is composed of a fiber loop mirror with additional intra-loop elements: a 3-dB optical coupler, a wavelength division multiplexer (WDM), a polarization controller (PC), an optical bandpass filter (BPF), and a nonlinear semiconductor optical amplifier (SOA) as the nonlinear element that is offset from the loop midpoint by a distance Δx. The operation principle of the TOAD can be described with the help of Fig. 1(b). A train of ultrashort optical clock pulses from the MLL are coupled into TOAD by a WDM as the control light; at the same time, the sampled continuous-wave as the signal light enters the loop via a 50:50 optical coupler and splits into two signals: a clockwise (CW) and a counterclockwise (CCW) propagating signal. Because the SOA is located at a certain distance Δx away from the fiber ring center, 34-36 the two counterpropagation light will successively arrive at the SOA, thus forming a delay window (a sampling or switching window). Specifically, when a control optical clock pulse reaches the SOA, the SOA reaches the gain saturation state and then gradually recovers. As a result, the two counter-propagation signal components experience a different phase modulation when they pass through the device before and after the clock pulse, respectively. Otherwise, they are affected by the same phase modulation. The two different conditions allow us to obtain two different transmission values, thus forming a sampling window with a time length Δt = 2Δx/vg (vg represents the group-velocity of the two counterpropagating signals in the fiber loop). During operation, the sampling window is opened periodically with the arrival of an optical clock pulse, so the input waveform can be sampled at the clock repetition. Finally, using a BPF, we can separate the sampled output from the optical clock because their operating wavelengths are different. In our study, the filtered amplified ASE is first coupled into the TOAD by a 50:50 optical coupler and then split into two equal beams in the CW and CCW direction, respectively. Meanwhile, a series of picosecond optical clock pulses originating from an ultrafast MLL are injected into the TOAD via a wavelength division multiplexer (WDM), which can periodically switch the sampling gate so that the ASE noise will be sampled at the clocking rate. After that, the separation of the sampled ASE pulses is finally realized by using a BPF near the output port of the TOAD.
In this experiment, the nonlinear SOA (Kamelian, SOA-NL-L1-C-FA) with a gain recovery time of 25 ps is biased at 300 mA and operates at a peak gain wavelength of 1550 nm and a 3-dB bandwidth of 64 nm. The MLL (Pritel, UOC-05-14G-E) with a timing jitter smaller than 50 fs operates at 10 GHz, and its wavelength is tuned to be 1551.2 nm. The BPF works at a center wavelength of 1553.7 nm with a 3-dB bandwidth of 0.6 nm, corresponding to that of the sampled output, so the sampled output can be separated from the sampling optical clock [as shown in the bottom right of Fig. 1(b)]. Quantitatively, the sampling output Pout roughly satisfies Pout ∝ P in [G CW + G CCW − 2 ⋅ (G CW ⋅ G CCW ) 1/2 ⋅ cos(Δφ)], where P in represents the power of the ASE noise signal to be sampled and G CW and G CCW denote the gains that CW and CCW ASE noise signals achieved through the SOA, respectively. The phase shift Δφ experienced by CW and CCW is controlled by the optical clock. The constructive interference occurs only when Δφ equals π, and thus, the ASE noise signal can be sampled. To guarantee this π phase shift, the average power of the optical clock pulse is set about −10 dBm in our experiment. By comparing Figs clearly that the continuous-time envelope of the sampled analog ASE noise [ Fig. 3(a)] matches well with the peaks of the discrete-time ASE pulses [ Fig. 3(b)], which confirms the high fidelity of the sampling operation. Herein, to illustrate the sampling results clearly, the sampled ASE noise is divided into two beams by a 90:10 optical coupler: 90% is fed into the TOAD to be sampled and subsequent quantization, while 10% is used as a reference path, which is convenient for us to compare with the final sampling results [i.e., red temporal waveforms in Fig. 3(b)]. Both beam signals are synchronously recorded by using a multi-channel real-time oscilloscope. However, one point should be noted here is that in order to better real-time synchronously observe the two beam optical signals, it is necessary to select appropriate optical delay lines to adjust the transmission length of the two beam optical signals.
In addition, the sampling linearity has also been evaluated in our experiment to quantitatively estimate the sampling fidelity. Figure 4 depicts the relationship between the amplitude of the sampled output signal and the power of the input signal to be sampled in our TOAD-based all-optical sampler. The solid mark is experimental data with a fitted line. After calculation, the linearity R 2

FIG. 4. Linearity evaluation of the TOAD-based all-optical sampler.
of the sampling process is as high as 0.997. This means a high fidelity.
In fact, the applied optical sampler (TOAD) can not only achieve a high-fidelity sampling but also improve the amplitude of the sampled ASE noise due to the gain compensation effect of the SOA. The sampled ASE noise with amplified amplitude (that is when the output is an optically sampled pulse, the corresponding pulse amplitude will fluctuate largely) is highly beneficial for subsequent quantization and random number exaction. To prove the correctness of this point, we have made several relevant statistical analyses on the amplitude distributions of the ASE signal before and after the TOAD, as shown in Fig. 3. To clarify this point more directly, we plot the amplitude distribution of the ASE noise before and after optical sampling, as shown in Fig. 5. The amplitude distribution is plotted using 1.6 × 10 6 data points. From this, one can observe that there exists a good linearity between the original and the optically sampled noise. After calculation, their evolution relationship can be expressed as Y = 2.48X + 51.56, where X and Y represent the time series of the noise before and after optical sampling, respectively. In addition, we evaluate the deviations between the ideal and the real sampled points using the mean square error (MSE). Calculated results indicate that the MSE is at a very low level about 4.3 × 10 −4 . Thus, we confirm that our optical sampling method can significantly improve the amplitude of the sampled ASE signal, which is very helpful to avoid the participation of complex post-processing.

C. 8-bit parallel comparator
An 8-bit parallel comparator embedded in the 36 GHz realtime serial data analyzer has been employed to quantize the optically sampled pulses. Here, to clearly explain the quantizing process, we take a 3-bit quantization as an example to illustrate the operation principle in our experiment. As shown in Fig. 6, the green curves represent the resulting time series of the sampled pulses; the seven gray dotted lines indicate the seven different decision thresholds of a 3-bit quantizer. The number of recorded samples is 1.6 Mbits. Combined with these decision thresholds, the peak point of the sampled pulses (marked with red asterisk in Fig. 6) can be divided into 3-bit binary codes, which agrees strongly with the corresponding threshold interval, as labeled in the vertical coordinate on the right side of Fig. 6. As expected, the entire amplitude range of the sampled pulses, under such a condition, will be mapped into eight strips. Then, in accordance with binary coding, each strip from bottom to top can be coded into "000," "001," "010," "011," "100," "101," "110," and "111," respectively. The 3-bit binary codes shown in Fig. 6 from the right column to left column correspond to D 0 , D 1 , and D 2 output from the 8-bit parallel comparator in Fig. 1(c). Thus, for a 3-bit quantizer, D 0 and D 2 are considered as the LSB and the most significant bit (MSB), respectively. The decimal digitization levels corresponding to the 3-bit binary codes are labeled in the vertical coordinate on the left side of Fig. 6.

III. QUANTUM RANDOMNESS EVALUATION AND EXTRACTION
As mentioned earlier, the raw random bits from our QRNG are generated by both the quantum noise and the classical noise. To date, extensive methods for extracting the randomness have been applied to quantum random bit generation, such as the min-entropy evaluation, 28,29 the Toeplitz-hashing algorithm, 4,30 the Trevisan's extractor, 31,37,38 and even the constructed physical model. 39,40 Herein, the extractable randomness of the raw data X is quantified by the worstcase min-entropy conditioned on classical side information E, 30,32 where P X/E (xi|e) is the discretized conditionally probability distribution of xi ∈ X. When the measurement output follows Gaussian distribution, Eq. (1) can be simplified as . R (i.e., R = 4.4σQ) equals to half of the input of the quantizer module and δ = 2R/(2 n ), where n (i.e., n = 8) is the sampling precision. σQ indicates the value of the standard deviation of quantum noise. The maximum classical noise excursion is chosen to be emax = 5σE (σ 2 E = the variances of classical noise) with 99.9999% confidence level. 30,32 We simplify the analysis progress and ensure that the system works under safety condition that c 1 = 0.0137 ≥ c 2 , in which the comparison between c 1 and c 2 will indicate whether the min-entropy evaluation utilizes the correct maximum guessing probability. In this case, H min (X|E) is estimated to be 6.19 bits per sample.
In the post-processing stage, the Toeplitz algorithm is employed as the randomness extractor to eliminate the classical noise and improve the statistical quality of the random numbers. [41][42][43][44] Given an m × n binary Toeplitz matrix, m random bits are extracted by multiplying the Toeplitz matrix with n raw bits. A true random sequence with a length of n + m − 1 bits is required and prestored to build the m × n binary Toeplitz matrix. In order to further optimize the extracting process, we choose m = 1024 and n = 1360 > 1024 × 8/6.19. According to the leftover hash lemma m = n ⋅ H min (X|E )/8 − 2 log 2 (1/ε), the corresponding security parameter ε is calculated as . Finally, the bit rate of the presented QRNG has the potential to be over 40 Gbps.
Note that a true random bit stream should be strictly unbiased and mutually independent.   45 to examine the obtained random bit (a 40 Gb/s sequence by reserving 4-LSBs sampled at 10 GSa/s). As advised by the NIST, each test is performed using 1000 × 1 Mbits with a statistical significance level α = 0.01. The test criterion for "success" is that the P-value (uniformity of p-values) should be larger than 0.0001 and the proportion should be within the range of 0.99 ± 0.009 439 2. Note that the P-value is the probability that a perfect random number generator would have produced a sequence less random than the sequence that was tested, given the kind of non-randomness assessed by NIST tests. For tests that return multiple P-values and proportions, the worst case is depicted in Fig. 8, in which the left and right ordinates represent the P-value and the proportion of each test, respectively. The typical test results indicate that the random number sequences obtained from our QRNG can well pass all the NIST tests.

IV. DISCUSSIONS
We want to point that using parallel processing could greatly enhance the potential for further improving the QRNG rate. Obviously, one can easily extended the wide-spectra ASE signal into many independent random sources utilizing the spectrally sliced technique. According to the requirements for parallel random number generation, 46 the spectrally sliced sub-entropy sources should be independent of each other. Here, we only take one case of them as an example to illustrate this point. Figures 9(a) and 9(b) depict the RF spectra and the cross-correlation function (CCF) of the two different filtering channels' outputs. Each of the channels' filtering bandwidths is 0.6 nm, and their center wavelengths are λ 1 = 1553.7 nm and λ 2 = 1554.5 nm, respectively. In our experiment, the time series of the two channels are simultaneously recorded at a sampling rate of 80 GSa/s for 0.2 ms, which is equivalent to a sample size of 16 Mbits. As shown in Fig. 9(a), all the RF spectra are very wide and flat. Such performance is beneficial for subsequent high-speed random bit extraction. From the CCF curve in Fig. 9(b), one can observe that the cross-correlation coefficient level is near zero. This indicates there is no inter-channel correlation between the temporal waveforms of the two different spectral components in the SLD. This guarantees the independence of different subsequences at the source.
In our current experimental system, a single-channel filtering scheme is successfully implemented where we use only one filtering channel and consume no more than 0.6 nm. Considering that the 3-dB spectral width of the whole SLD is at least 55 nm, we believe that utilizing some extra filtering devices, the number of parallel wavelength channels can be increased to at least 90. In view of this point, our QRNG is expected to achieve an accumulative bit rates up to Tb/s.
Herein, we note that our proof-of-principle experiment uses discrete photonic and electronic components so that the whole system is relatively bulky. Fortunately, the integrated MLL and TOADbased optical sampling gate have been reported with the advanced photonic integrated circuits (PICs) in recent years. [47][48][49] If the PIC techniques are introduced to design the QRNGs, our scheme may be monolithically integrated and thereby provide a highly compact device. One of our future works is to combine the PIC technology with quantum random bit generation.

V. CONCLUSIONS
In conclusion, we proposed and experimentally demonstrated a fast QRNG based on optically sampled ASE. In our proof-ofprinciple experiment, a low-complexity TOAD-based optical sampler is first introduced to perform the optical sampling function for fast quantum random number generation. Then, an 8-bit parallel comparator is used to digitize the obtained optically sampled pulses. Finally, by reserving four LSBs sampled at 10 GSa/s, a 40 Gb/s random bit sequence can be continuously obtained. Moreover, we also apply the min-entropy and the Toeplitz hashing to further evaluate and extract the quantum randomness. In contrast to electrical sampling, our approach can efficiently overcome the electronic jitter bottleneck. Thus, this proposal provides one way of combining photonic signal processing with ultrafast quantum random numbers, which might also be a good alternative to conventional postprocessing QRNGs employing electrical ADCs. In addition, with the rapid development of the PIC technology, it may allow us to explore more monolithically integrated QRNGs for future practical applications.

AUTHORS' CONTRIBUTIONS
Y.G. and Q.C. contributed equally to this work.