Random numbers are widely used in cryptography [1], scientific simulation and computing [2], and many other fields. However, commercial random number generators (RNGs) currently face security problems in practical applications since they originate from the deterministic transformation and are predictable. In contrast, hardware RNGs based on physical processes, such as noise in electronic devices, nuclear fission, circuits, and radial decay [3–6], are believed to provide better random numbers, but it is unclear whether they can also be predicted since they are made of complex physical processes.

Quantum resources, which have natural uncertainties, are very suitable for RNG production, that is, quantum RNG (QRNG). Existing QRNG methods include single-photon detection, vacuum state fluctuations, and quantum phase fluctuations [7–10]. These QRNGs can be commercialized and deployed in many scenarios. The rise of integrated quantum technology provides a bright prospect for realizing miniaturized, compact, highly stable, scalable, and portable QRNGs, especially showing significant advantages in the size reduction of QRNG systems [11–14]. Recently, much progress has been made in integrating QRNGs [15–20].

However, hackers may control the quantum resources, causing severe security issues in all the current on-chip QRNG systems [21–24]. The device-independent (DI) scheme offers a drastic solution to the security issues of QRNGs [25–27], but the experimental realization conditions of the loop-free Bell test are harsh, and the bit rate is low [28–32]. Since the measurement devices are often simple and characterizable, the source-device-independent (SDI) approach perfectly balances the potential security risks of QRNGs and the intractability of DI scheme [21–23]. In the SDI scenario, the measurement device is assumed to be trusted, and the source is untrusted. Recently, many SDI-QRNG schemes have been proposed [33–40], solving the common security issues faced by sources in QRNG and making it secure regardless of whether hackers control the quantum resources.

Integrating SDI-QRNG is the crucial step toward its application due to silicon-based photonics chips being ideal platforms for large-scale low-cost secure utilization at room temperature, which can greatly address the practical security risks faced by the current QRNG chips [12,41]. However, it is challenging to simultaneously guarantee the on-chip efficient utilization of quantum randomness and on-chip security of QRNG devices. Specifically, for the on-chip randomness of QRNG, realizing the on-chip high-speed and undistorted detection of quantum resources is one challenge, determining how much quantum entropy the generator can obtain. For the security of QRNG, bounding the amount of on-chip practical side channel information through a practical chip-level physical system is complex, which determines how much randomness remains secure. To the best of our knowledge, no SDI-QRNG chips have been reported so far due to the above difficulties in on-chip implementation.

In this paper, we propose an on-chip SDI-QRNG scheme that maintains the randomness in chip realization and provides security entropy evaluation criteria in a practical QRNG system, which is necessary because the chip cannot be disassembled and changed like the discrete scheme after implementation. Subsequently, a chip-level SDI-QRNG optical platform was implemented. The high-bit-rate randomness is acquired by a high-bandwidth distortion-free on-chip coherent detection and noise elimination. The security is guaranteed by maximizing the estimation of eavesdropping entropy due to the random fluctuation deviation of measurement base selection. The SDI-QRNG is integrated into a photonic circuit with a size of $2.9\mathrm{mm}\times 4.5\mathrm{mm}$ by adopting micro-nano photonics integration technology, and the highest limit of 248.47 Gbps on the secure bit rate can be achieved by this on-chip generator owing to high bandwidth on-chip detection up to 27.7 GHz. Moreover, a secure bit generation rate of 146.2 Mbps was achieved by the practical SDI-QRNG system with an integrated photoelectric package, with all the extracted secure bits passing the randomness test. Our work verified the feasibility of on-chip implementation of SDI-QRNG in principle, paving the way for the large-scale low-cost application of quantum resources at room temperature, which is advanced progress in the QRNG area.

Our on-chip SDI-QRNG scheme is shown in Fig. 1. This scheme is based on the coherent detection of the vacuum state. To ensure the security of the random number generation according to the entropic uncertainty principle (EUP), we modulate the LO by a PM to achieve the on-chip random measurement basis switching, which was proposed and proven secure by Marangon et al. in 2017 [22]. Therefore, both randomness and security can be guaranteed in our SDI-QRNG chip. Next, we will explain how to realize the randomness and security of chips.

To maintain randomness on the QRNG chip, quantum randomness generation, distortion-free quantum detection, and noise interference elimination are required. For the QRNG system based on the vacuum state fluctuation, the Heisenberg uncertain relationship between the non-commutative physical quantities quadrature components $P_m$ and $Q_m$ of the $m$th arbitrary quantum state can be obtained: $$⟨{(\mathrm{\Delta }{\widehat{P}}_m)}^2⟩⟨{(\mathrm{\Delta }{\widehat{Q}}_m)}^2⟩\ge \frac{1}{4}{|⟨[{\widehat{P}}_m,{\widehat{Q}}_m]⟩|}^2=\frac{1}{16}.$$(1)The above equation shows that neither of the two quadrature components can be accurately measured simultaneously in any quantum state. Based on the basic principle of quantum mechanics, the randomness of on-chip quantum resources is guaranteed.

For the QRNG scheme based on vacuum states, homodyne detection is used. The relation between the annihilation operator and the quadrature component is $\widehat{\alpha }=\frac{1}{2}({\widehat{P}}_m+i{\widehat{Q}}_m)$, where $m$ represents the $m$th quantum state, and the vacuum state $|\alpha ⟩=|0⟩$ is employed as the source in SDI-QRNG. Moreover, as a classical light field, the LO can be expressed as ${\alpha }_{\mathrm{LO}}=|{\alpha }_{\mathrm{LO}}|e^{i\theta }$. Then the LO and the vacuum state enter the MMI splitter with the transmittance of 1/2 through two input ports, and the output two light field modes are [42] $$S_{\mathrm{MMI}}(1/2)\left[\begin{array}{c}\widehat{\alpha }\\ {\alpha }_{\mathrm{LO}}\end{array}\right]=\left[\begin{array}{c}\frac{1}{\sqrt{2}}(\widehat{\alpha }+{\alpha }_{\mathrm{LO}})\\ \frac{1}{\sqrt{2}}(\widehat{\alpha }-{\alpha }_{\mathrm{LO}})\end{array}\right]=\left[\begin{array}{c}{\widehat{\alpha }}_1\\ {\widehat{\alpha }}_2\end{array}\right],$$(2)where ${\widehat{\alpha }}_1$ and ${\widehat{\alpha }}_2$ are annihilation operators of the two output optical field modes. The photon number operator at the output can be calculated as $$\begin{gathered} {\widehat{n}}_1\begin{array}{c}={\widehat{\alpha }}_1^{†}{\widehat{\alpha }}_1=\frac{1}{2}({\widehat{\alpha }}^{†}\widehat{\alpha }+{\alpha }_{\mathrm{LO}}^{*}{\alpha }_{\mathrm{LO}}+{\alpha }_{\mathrm{LO}}{\widehat{\alpha }}^{†}+{\alpha }_{\mathrm{LO}}^{*}\widehat{\alpha }),\hfill \end{array} \\ {\widehat{n}}_2={\widehat{\alpha }}_2^{†}{\widehat{\alpha }}_2=\frac{1}{2}({\widehat{\alpha }}^{†}\widehat{\alpha }+{\alpha }_{\mathrm{LO}}^{*}{\alpha }_{\mathrm{LO}}-{\alpha }_{\mathrm{LO}}{\widehat{\alpha }}^{†}-{\alpha }_{\mathrm{LO}}^{*}\widehat{\alpha }), \end{gathered}$$(3)and $\mathrm{\Delta }\widehat{n}={\widehat{n}}_1-{\widehat{n}}_2=|{\alpha }_{\mathrm{LO}}|({\widehat{P}}_m\cos \theta +{\widehat{Q}}_m\sin \theta )$. Since the measured value depends on the phase $\theta$ of the LO, the output can be directly proportional to the quadrature component by controlling the phase, which means that $\mathrm{\Delta }\widehat{n}=|{\alpha }_{\mathrm{LO}}|{\widehat{P}}_m$ for $\theta =0$ and $\mathrm{\Delta }\widehat{n}=|{\alpha }_{\mathrm{LO}}|{\widehat{Q}}_m$ for $\theta =\pi /2$. After photocurrent conversion by PDs, the differential current output of the detector is $\mathrm{\Delta }{I}_m=\beta |{\alpha }_{\mathrm{LO}}{\widehat{\alpha }}^{†}+{\alpha }_{\mathrm{LO}}^{*}\widehat{\alpha }|$, where $\beta$ is the amplification factor of the cross-resistance amplifier, and $\mathrm{\Delta }{I}_m$ satisfies $⟨\mathrm{\Delta }{I}_m⟩=0$ and $⟨\mathrm{\Delta }{I}_m^2⟩={\beta }^2{|{\widehat{a}}_{\mathrm{LO}}|}^2$. The fluctuations of the output photocurrent mainly come from the fluctuations of the vacuum state. Therefore, the fluctuations of the vacuum state can be measured from $\mathrm{\Delta }{I}_m$ to generate the quantum random numbers.

For the security of on-chip SDI-QRNG, we mainly consider how to realize the secure entropy evaluation in the practical situation. In theory, Marangon et al. proposed to use EUP to evaluate the maximum amount of information that Eve may obtain. According to EUP, a lower secure bound of the quantum conditional minimum entropy of the system with discrete components has been proposed [22], which is also well known as a self-testing scheme [23].

The secure bound of quantum conditional minimum entropy of SDI-QRNG provided by Marangon et al. is $H_{\mathrm{low}}\equiv -{\log }_{2}u(\delta q,\delta p)-H_{\max }(Q_{\delta q}|B)\le H_{\min }(P_{\delta p}|E)$. To better estimate the practical quantum conditional minimum entropy of the on-chip SDI-QRNG system, the practical on-chip quantum conditional minimum entropy $H_{\mathrm{low}}^{\mathrm{pra}}$ can be defined as $$\begin{gathered} H_{\mathrm{low}}^{\mathrm{pra}}\equiv -{\log }_2{u}_{\mathrm{pra}}(\delta q,\delta p)-H_{\max }^{\mathrm{pra}}(Q_{\delta q}|B) \\ \le H_{\min }^{\mathrm{pra}}(P_{\delta p}|E), \end{gathered}$$(4)where $P_{\delta p}$ and $Q_{\delta q}$ represent the measurement results obtained by detecting the quadrature components $P$ and $Q$ at resolutions $\delta p$ and $\delta q$, respectively, for quantum states that may be controlled and shared by Eve. And $u_{\mathrm{pra}}(\delta q,\delta p)=\frac{1}{2\pi }\delta q\delta p{S}_0^{(1)}{(\frac{\delta q\delta p}{4},1)}^2$ represents the incompatibility of the measurement operators, and $S_0^{(1)}$ is the 0th radial prolate spheroidal wave function of the first kind. And theoretical data resolution is $\delta p=\delta q=\frac{U_{{\mathrm{\Delta }}_{\mathrm{range}}}}{2^n}$, where $n$ is the bit width, $2^n$ is the bit resolution, and $U_{{\mathrm{\Delta }}_{\mathrm{range}}}$ is the quantized voltage measurement range. The practical conditional max-entropy $H_{\max }^{\mathrm{pra}}(Q_{\delta q}|B)$ expresses Bob’s lack of practical knowledge about $q_{m_k}$.

Considering the practical imperfections such as the modulation signal fluctuation of the PM, and the non-uniform change of carrier concentration, a phase modulation bias ${\delta }_{\theta }$ will be inevitably introduced in the phase space when implementing a $\pi /2$ phase shift on the vacuum state. This on-chip measurement base selection bias will be more severe than the discrete bulk one due to limitations by the implementation conditions. Since this deviation is caused by the comprehensive influence of multiple independent tiny various factors, the deviation ${\delta }_{\theta }$ can be reasonably assumed to follow the Gaussian distribution $N_{{\delta }_{\theta }}(0,{\sigma }_{{\delta }_{\theta }}^2)$. The max-entropy $H_{\max }^{\mathrm{pra}}(Q_{\delta q}|B)$ reduces to $H_{\max }^{\mathrm{pra}}(Q_{\delta q_{m_k}^{\prime }})$ because the legal parties are the same as the one in QRNG, and it can be written as $$H_{\max }^{\mathrm{pra}}(Q_{\delta q_{m_k}^{\prime }})=\underset{\{q_{m_k}^{\prime },{\delta }_{{\theta }_m}\}}{\max }\left[2{\log }_2\sum _k\sqrt{\mathfrak{p}\left(\frac{q_{m_k}^{\prime }}{\cos {\delta }_{{\theta }_m}}\right)}\right],$$(5)where ${\widehat{q}}_m=\frac{{\widehat{q}}_m^{\prime }+{\widehat{p}}_m\sin {\delta }_{{\theta }_m}}{\cos {\delta }_{{\theta }_m}}$ and $\mathrm{\Delta }{\widehat{q}}_m^{\prime }=-{\widehat{p}}_m\sin {\delta }_{{\theta }_m}$. As ${\delta }_{{\theta }_m}$ is very small (generally less than 1°), ${\widehat{p}}_m\tan {\delta }_{{\theta }_m}\ll \frac{{\widehat{q}}_m^{\prime }}{\cos {\delta }_{{\theta }_m}}$, therefore ${\widehat{q}}_m\approx \frac{{\widehat{q}}_m^{\prime }}{\cos {\delta }_{{\theta }_m}}$, ${\delta }_{{\theta }_m}$ follows Gaussian distribution $N(0,{\sigma }_{{\delta }_{{\theta }_m}}^2)$, and $H_{\max }^{\mathrm{pra}}(Q_{\delta q_{m_k}^{\prime }})$ is the maximum practical potential information bound for any $\{q_{m_k}^{\prime },{\delta }_{{\theta }_m}\}$ obtained by Eve in the practical on-chip system. According to the Laida rule, $P\{|{\delta }_{\theta }|<3{\sigma }_{{\delta }_{\theta }}\}=99.73\%$, and the phase drift ${\theta }_{\mathrm{dev}}$ can be reasonable to be assumed as ${\theta }_{\mathrm{dev}}<1°$; therefore $P\{|{\sigma }_{{\delta }_{\theta }}|<1/3°\}=99.73\%$, where ${\theta }_{\mathrm{dev}}$ represents the maximum upper bound of the deviation of the modulation angle in the actual experiment, ${\delta }_{\theta }$ represents the deviation of the modulation angle in the actual experiment, and ${\sigma }_{{\delta }_{\theta }}$ represents the variance of the angle deviation variable. In the practical case, the $u_{\mathrm{pra}}(\delta q,\delta p)=\frac{1}{2\pi }\delta q\delta p{S}_0^{(1)}{(\frac{\delta q\delta p}{4},1)}^2$ should also be replaced by $u_{\mathrm{pra}}^{\prime }(\delta q^{\prime },\delta p)=\frac{1}{2\pi }\delta q^{\prime }\delta p{S}_0^{(1)}{(\frac{\delta q^{\prime }\delta p}{4},1)}^2$, where $\delta q^{\prime }=\frac{{\delta }_q}{\cos {\delta }_{{\theta }_m}}$. For the practical realization of the on-chip SDI-QRNG scheme, we take into account also the finite-size effects by using the smooth min-entropy that can be bounded as $$H_{\mathrm{low}}^{{ϵ}_{\mathrm{pra}}}(P_{\delta p}|E)\equiv H_{\mathrm{low}}^{\mathrm{pra}}(P_{\delta p}|E)-\frac{1}{\sqrt{n_P}}{\mathrm{\Delta }}_{\mathrm{pra}},$$(6)with ${\mathrm{\Delta }}_{\mathrm{pra}}=4{\log }_2(2^{\zeta }+1)\sqrt{{\log }_2(2/{ϵ}_{\mathrm{pra}}^2)}$, where $\zeta =1+H_{\max }^{\mathrm{pra}}(Q_{\delta q_{m_k}^{\prime }})/2$, $n_P=m-n_Q$ is the number of measurements for the data quadrature, and ${ϵ}_{\mathrm{pra}}$ is the security parameter. The whole process of how the scheme runs can be summarized in Fig. 2.

The above scheme can solve the inevitable practical security problem caused by the on-chip devices with imperfect realistic conditions. It can help us evaluate more accurate security entropy in actual implementation. Therefore the above model is applicable for the presence of nonperfect factors in on-chip SDI-QRNG when it cannot be disassembled during actual chip implementation.

From the consideration of implementing an efficient and secure SDI-QRNG chip, our SDI-QRNG chip system mainly consists of on-chip wide bandwidth detection of quantum resources and on-chip high-precision measurement basis switching with low half-wave modulation voltage.

To realize the high fidelity of on-chip quantum state detection in QRNG, a silicon-based germanium detector with a large bandwidth is realized to implement distortion-free detection, which means that the two adjacent sampling data will not affect each other. In the experiment, since the sampling signal is always within the detection bandwidth, the randomness distortion-free detection is realized. The setup to characterize the bandwidth of photodetector performance is shown in Fig. 3(a), where the input light source is a 1550 nm continuous optical laser. First, the changed RF signal is modulated to the wave amplitude as the light passes through an MZM (OSC-MOD-40Gb-460C). The RF signal is generated from the vector network analyzer (VNA, Anritsu MS46522B). The Ge absorption layer material is directly connected with the silicon waveguide, and the modulated light is directly coupled with the Ge absorption layer at the upper end by evanescent-field coupling. The modulated light is amplified by the erbium-doped fiber amplifier (EDFA) with adjustable gain before entering the PD on the chip. The electrical signals generated by the detector are separated into DC and AC signals by bias-tee. The AC signal demodulated by the detector is input into the VNA to complete the test of S21 parameters. As shown in Figs. 3(b) and 3(c), corresponding to the testing chip with the DC gold wire package and the bare chip without a package, the electro-optic S21 3 dB bandwidth of the Ge vertical photodetector is about 16.3 MHz and 27.7 GHz, under the reverse bias voltage of $-1\mathrm{V}$. And the on-chip detection responsivity of 0.81 A/W and a high equivalent quantum efficiency of 64.87% were finally realized. The on-chip detector has excellent linearity in the working area, which is important for the reliability of final randomness and has been fully tested and shown in Appendix A.

To further improve the scheme efficiency, an on-chip modulator with high-precision measurement base selection should be implemented to greatly reduce the impact of system bit rate performance caused by the imperfection. To ensure practical security and obtain better system performance, the low and stable half-wave voltage $V_{\pi }$ of the on-chip phase modulator should be implemented to achieve high-precision measurement base selection easily. We implemented the on-chip PM modulator with half-wave voltage $V_{\pi }=3.7\mathrm{V}$, and since high-precision measurement base selection can be easily realized and ${\delta }_{{\theta }_m}$ is small, this further reduces the impact of bit rate performance caused by the on-chip imperfect measurement base selection (see details in Appendix A).

Figure 4(a) shows the schematic diagram of the SDI-GRNG chip for the experiment, and Fig. 4(b) shows that PDs are implemented with a size of $16\mathrm{\mu m}\times 23\mathrm{\mu m}$ for light detection based on Ge PIN PD. The LO was a narrow line 1550 nm laser coupled to the chip by vertical GCs and then through a PM driven by an AWG. The AWG supplies secure random bits to control the PM when generating the selection signal of the measurement basis of the check quadrature $Q_{\delta q}$. Meanwhile, the LO and vacuum states pass through a 50:50 MMI splitter and enter PDs after interference. The output of the PDs was monitored by a DSO. The output difference current signal was then sampled by an oscilloscope, which sent multiple acquisitions of $m$ samples of each frame to a PC for post-processing. Part of the SDI random number obtained by the PC is directly used to control the random selection of the measurement base by the PM.

For basis switching, we set a ratio of 1/10 between the number of check measurements $n_Q$ and total samples $m$. An initial random seed was preinstalled into the AWG to decide whether to start from check measurements or data measurements. Figure 5(b) shows that the switching signal of the quadrature component is applied to PM. 3.7 V is the half-wave voltage of the PM, and when 1.85 V is applied to PM, the phase of the signal light will rotate by 90°, at which time the $Q$-quadrature component will be measured at the detection end with 250 kHz modulation voltage switching frequency.

For detection, a high-speed oscilloscope with 2.5 GHz bandwidth and 10 GS/s sampling rate is used for sampling. The electrical signal before sampling is within the oscilloscope’s operating range and therefore has a linear relationship with the quantized data. The nonlinearity of the analog-to-digital converter (ADC) may not have a significant impact on the measurement accuracy of the quadrature $P$ that is used to generate the raw random numbers, due to a relatively small range and a 10-bit high ADC resolution. However, in the actual measurement, classical noise, such as classical electronic noise and relative intensity noise of a laser, will inevitably be introduced into the measurement system. Therefore, the chip-detection signal ${\sigma }_{\mathrm{chip}}^2$ includes quantum noise ${\sigma }_q^2$ and classical noise ${\sigma }_c^2$, namely ${\sigma }_{\mathrm{chip}}^2={\sigma }_q^2+{\sigma }_c^2$, in which ${\sigma }_{\mathrm{chip}}^2$ represents the chip-detected randomness, ${\sigma }_q^2$ represents quantum nature randomness, and ${\sigma }_c^2$ represents the randomness introduced by chip imperfections. Figure 5(a) shows the data quadrature $P_{\delta q}$ and check quadrature $Q_{\delta q}$. Due to the RF signal crosstalk between the gold wires, there is an impact interference on the quadrature component $Q_{\delta q}$, the impact interference on the $Q_{\delta q}$ will also be equivalently treated as the noise introduced by the eavesdropper according to the scheme, and finally, the secure random bit stream can be extracted by compression.

After basis-switching and on-chip vacuum state detection, we can obtain that the quantum conditional min-entropy of each frame is about 9.42 bits/sample in this frame according to Eq. (4). Considering the finite-size effect, the quantum conditional min-entropy under 250 kHz switching frequency is shown in Fig. 6 according to Eq. (6). To distill the secure random bits with more rigorous practical security, we choose the minimal quantum conditional min-entropy of the 50 frames under 250 kHz after considering the finite size effect as the conservative evaluation of the quantum conditional min-entropy used to generate the final secure random bits. Specifically, the highest min-conditional entropy is $H_{\mathrm{low}}^{ϵ}(P_{{\delta }_{10}}|E)=8.97\pm 0.01$ bits per measurement for total data points $m_0=5\times {10}^5$ with secure parameter ${ϵ}_{\mathrm{pra}}{=10}^{-6}$. After randomness extraction, our on-chip SDI-QRNG system can achieve $R=16.3\text{MS/s}\times 8.97\text{bits/sample}=146.21\mathrm{Mbps}$ secure bit rate with an integrated photoelectric package, and all the extracted secure bits can pass the randomness test. Additionally, we choose a middle conservative sample rate 27.7 GS/s to calculate the highest theoretical limit of the secure bit generation rate, and it is $R_H=27.7\text{GS/s}\times 8.97\text{bits/sample}=248.47\mathrm{Gbps}$ due to the bare chip detection bandwidth being 27.7 GHz (see Appendix A for details).

The above results show that this SDI-QRNG chip can generate quantum secure random numbers continuously. Moreover, once the high-frequency signal transmission limitation in packaging is solved, the theoretical secure random number rate can reach 248.87 Gbps under the highest practical detection bandwidth 27.7 GHz in the bare chip. Such a random number generation rate can fully meet data security encryption requirements, such as the one-time pad encryption algorithm. In addition, the miniaturized chip can also be placed in classical communication devices as a module to ensure data security.

The advantages of the work we present are as follows. (i) We have considered the practical security issues of the SDI-QRNG system for the first time, especially in the special physical environment of chip-level SDI-QRNG systems with non-detachable characteristics, and proposed a framework that can guarantee the practical security of the system through post-processing. (ii) Secondly, we have realized that the first simple and efficient secure SDI-QRNG chip optical platform, which overcomes the problem of simultaneously integrating high-precision PM and large bandwidth on-chip detection up to 27.7 GHz on a single chip with low power consumption, can meet the strict requirements of SDI-QRNG chip systems for on-chip manipulation and detection of quantum states. (iii) The implementation of this scheme is different from other existing DI schemes that require low-temperature superconducting nanowire detectors. It has a simple structure based on shot-noise limit detection, which is conducive to low-cost and large-scale implementation and deployment, paving the way for the large-scale application of quantum resources at room temperature.

The practical security guarantee of SDI-QRNG is a core challenge that must be considered to achieve large-scale secure applications of quantum resources, due to the nondetachable characteristic of SDI-QRNG chips. In addition, for the implementation of SDI-QRNG chips, it is crucial to have a dedicated on-chip PM that can adapt to the strict requirements of SDI-QRNG for high accuracy, high bandwidth, etc., as it determines the practical security of the chip SDI-QRNG. Meanwhile, the implementation of low half-wave voltage PM based on meeting the above requirements means low driving power consumption of SDI-QRNG, providing the possibility for further full integration and deployment in space science. Moreover, high on-chip detection bandwidth is also crucial as it determines the quality of randomness detection. Therefore, integrating both the PM and PDs on a single chip and meeting the stringent requirements of SDI-QRNG is urgently needed and important. We have overcome the above challenging issues and validated the feasibility of on-chip SDI-QRNG for the first time, which is fundamentally different from previous work [19,22,23,40] and advanced progress in the DI/SDI field.

In actual experiments, due to the advantages of our chip such as low-half wave voltage and stability, the maximum modulation angle deviation does not exceed 1°. The modulation angle deviation here is caused by the accuracy of the base selection when selecting the measurement base. Therefore, we mainly consider observing the actual accuracy of the base selection from the perspective of the half-wave voltage of the on-chip modulator. We have shown that the measured half-wave voltage of on-chip modulator in this experiment is 3.7 V in Appendix A, and the voltage we applied is the main source of nonperfection in the basis selection due to accuracy issues. The angle of deviation is determined by measuring the difference between the actual modulation voltage and the measured half-wave voltage. As the voltage we apply for base selection is also 3.7 V, considering other nonperfect factors such as voltage fluctuations and accuracy errors, we comprehensively calculate that it does not exceed 1°. In addition, in practical implementation, due to differences in the measurement deviation of half-wave voltage and the accuracy of the AWG, more imperfect modulation angles may be considered in practical scenarios based on the characterization of actual device performance. Moreover, recent researches reveal that the plasma dispersion effect may lead to phase deviation from expectations [43,44], which is included in our model, and ${\delta }_{\theta }$ in our model can reflect this situation.

For implementation, it is worth noting that the feedback for enhancing the randomness of the check measurement is controlled through the PC connection, which will hinder the further miniaturization of the system. Therefore, the device will be integrated photoelectrically using PCB integration in the next step. In addition, the balanced homodyne of the system is realized by subtracting the detected optical current at the oscilloscope. Using a trans-impedance amplifier (TIA) circuit with a low-noise amplifier and field programmable gate array (FPGA) for data processing will realize further photoelectric integration and miniaturization. Besides, the optimization implementation of the circuit also needs to be further considered to reduce the crosstalk of check quadrature and further reduce the impact of external interference on the system. Finally, as an essential part of SDI-QRNG, the on-chip light source that generates LO also needs to be integrated into the system in a hybrid way.

The core of achieving a high bit rate is divided into two steps. One is to achieve a high on-chip random bit generation rate, which is mainly guaranteed by high on-chip bandwidth. The second step is to achieve a high post-processing rate commensurate with the high on-chip random bit production rate, which is guaranteed by the high computing performance of the peripheral supporting electronic circuits. Therefore, by using high computational performance custom application-specific integrated circuits such as an FPGA or an application specific integrated circuit (ASIC), the high real-time secure rates can be reasonably implemented [20]. It can be seen that our on-chip detection bandwidth has reached 27.7 GHz, so the main limitation of the bit rate here is the gold wire packaging. Therefore, we will further use the latest technologies such as high-frequency packaging to ensure that the packaging bandwidth also reaches GHz, optimizes post-processing technology, and uses higher performance GPUs, ultimately achieving a bit rate of Gbps.

Compared to other classical on-chip QRNGs such as QRNGs based on chaotic optical frequency combs, all these QRNGs have the same advantages of miniaturization, which gives them the potential to be deployed on a large scale. This work is based on quantum mechanisms, so it has information theory provable security. Meanwhile, we have considered the practical security of the system in practical implementation, which makes it more rigorous in combating actual deployment security risks. The random number generator based on chaotic optical combs is classic, and the theoretical security proof needs to be improved and faces practical security issues. The SDI-QRNG chip has demonstrated the high bandwidth bit rate on the chip, which is a promising way to achieve the same progressiveness as classic QRNG chips.

Since the SDI-QRNG scheme is designed to overcome the situation where the source is untrusted, it is necessary to make reasonable assumptions about the trusted probe end of the system. Throughout the entire life cycle of our SDI-QRNG chip principle verification experiment, our detectors are completely under our control and will not be eavesdropped by Eve.

In this work, we have verified the feasibility of the on-chip implementation of an SDI-QRNG optical platform in principle and implemented this SDI-QRNG chip with secure entropy generation of 8.97 bits/sample and a secure random number rate of 146.2 Mbps under the practical package detection bandwidth 16.3 MHz with all the extracted secure bits passing the randomness test. The theoretical secure random number rate can reach 248.87 Gbps under the highest measured detection bandwidth 27.7 GHz in the bare chip. Such a random number generation rate can fully meet data security encryption requirements, such as the one-time pad encryption algorithm. Our work is advanced progress in the SDI-QRNG area and is also valuable for the large-scale, low-cost exploitation and efficient utilization of the physical properties of quantum resources at room temperature.