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An Integrated Silicon Photonic Chip for Continuous-Variable Quantum Random Numbers Generator Based on Vacuum Fluctuation

The deployment of quantum random number generator in fiber optics is strongly limited in real world applications due to the size of the components and their cost. Here we present a quantum random number generator based on vacuum fluctuation using an optical homodyne detection in silicon photonic chip achieving minimum entropy/bit of 8.5 for 10 bits sample. The produced random numbers have passed all NIST randomness tests.


Introduction
Random number is an essential resource for many applications, such as in simulation [1] and lotteries, especially classical and quantum cryptography [2,3]. However, with the development of computer science and technology, random numbers generated by mathematical algorithms and classical physical processes will cause safety issues in cryptography applications due to their intrinsic determinacy [4]. In contrast, random numbers generator based on quantum mechanics [5] can offer the ultimate in randomness. In the past few decades, quantum random number generators (QRNG) have made significant achievement using different quantum entropy sources including photon path [6], photon arrival time [7] , photon number distribution [8], vacuum fluctuation [9,11], phase noise [12,13], amplified spontaneous emission noise of quantum states [14], etc. QRNG can be divided into discrete type and continuous type according to different entropy sources. Compared with the discrete-variable QRNG, the continuous-variable QRNG (CV-QRNG) is easy to prepare entropy sources, has low requirements for detection devices, and has a high generation rate, so it can save a lot of cost and has a very broad application prospect. Typically, one of the most prominent optical CV-QRNG schemes is based on vacuum fluctuation for the simplicity and compactness of the experimental device and high random numbers generation rate. So far, the development of vacuum states QRNG has been very mature and the generation speed has met the current needs. Now the QRNG is gradually facing the application market. However, most of vacuum fluctuation QRNGs are usually realized using either with bulk or fiber components, which leads to strong limitations in real application because of the large size, high cost, instability and the difficulty of integrating into other complex systems. To dispose of this, silicon optoelectronic technology compatible with complementary metal oxide semiconductor (CMOS) craft has entered people's field of vision.
In recent years, the vacuum fluctuation QRNG [10] by using the homodyne detector integrated in silicon-on-insulator (SOI) has been experimentally realized. However, after equal interval quantization, the calculating minimum entropy/bit of 5.9 for 8 bits sample is relatively small in the experiment by Raffaelli et al [10]. In this paper, we use the homodyne detector integrated in SOI and the off-chip laser, the off-chip transimpedance amplifier (TIA) to independently build a vacuum states QRNG system. The scheme is simple, highly integrated and small in size. The minimum entropy achieved through equal probability quantization is 8.5 for 10 bits sample. The final produced random numbers pass all NIST [15] randomness tests.

Experiment realization
The experimental setup of QRNG based on vacuum fluctuation is depicted in Figure 1. The scheme consists of three sections, including the off-chip laser, the off-chip transimpedance amplifier (TIA) and the on-chip homodyne detector. The laser light emitted by an off-chip NKT laser with 1550 nm is used as the local oscillator (LO). The on-chip homodyne detector contains two grating couplers, three multi-mode interferences (MMIs), a thermo-optical phase shifter and two germanium p-i-n photodiodes (PD). The LO is coupled into the single mode waveguides through the pigtail and the vertical grating coupler. While the port of other grating coupler input the vacuum states as signal. The MMI as a beam splitter makes the signal interfere with the LO to amplify the weak vacuum signal. One of the output waveguide of the MMI which passes through Mach-Zehnder interferometer with a thermo-optic phase shifter in one arm is detected by PD. However, due to limited time, the experiment did not use a thermo-optic phase shifter. The other output port of the MMI is directly connected to the PD through waveguide. The photocurrents generated by the two photodiodes are input into the printed circuit board (PCB) through wire bonding and a TIA is used in the PCB to amplify the difference of the two photocurrents. The whole system including PCB and silicon chip is only a few centimeters square in size. The chip-based QRNG can reduce costs, achieve mass production, and is easier to integrate into other complex systems. In the measurement of vacuum states, some classical noise will be introduced due to various practical conditions. In order to remove the classic noise, the raw data needs to be post-processed. Following previous work [16], the quantum noise and classical noise all follow independent Gaussian distribution and the measured signal M is the superposition of classical noise E and quantum noise Q. The relation of their variances is 2 The classical noise can be measured in the absence of the LO. The range of the measurement signal is divided into 10 2 bins. Each bin has equal area and is assigned a fixed binary string of length 10, similarly to Figure 1(b) in the ref [9]. Compared with equal interval quantization, this quantization method is more accurate and achieves better results. However, the 10 bits number corresponding to each sample contains classical noise. In order to extract random bits generated by quantum signals, we need to use the min-entropy. For variable X with probability distribution () Xi Px, the minimum entropy is defined in unit as [17].
After obtaining the minimum entropy, the Toeplitz hashing method is used to extract random numbers that do not contain classical noise.

Results and analysis
To ensure that the random numbers can be extracted and the appropriate sampling rate can be obtained, the spectral power density of QRNG is measured when the power of LO is 0 and the maximum. The power spectral density is shown in Figure 2. Since the output optical power of the laser is directly coupled to the chip through the pigtail, the coupling efficiency is low and the laser optical power is relatively large. In addition, the low frequency spike on the black line may be related to the PD on the chip, but it does not affect uplift of the spectrum. The ratio of shot noise to electronic noise is near 11 dB. The fact approximately indicates that there are certain random numbers that can be extracted in the process of random extraction. The bandwidth range is near 20MHz and the corresponding sampling rate is 40MHz.