• Photonics Research
  • Vol. 12, Issue 7, 1379 (2024)
Lang Li1,2,3,†, Minglu Cai1,†, Tao Wang1,2,3,†, Zicong Tan1,2,3..., Peng Huang1,2,3, Kan Wu1 and Guihua Zeng1,2,3,4,*|Show fewer author(s)
Author Affiliations
  • 1State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2Institute of Quantum Sensing and Information Processing, School of Sensing Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • 3Shanghai Research Center for Quantum Sciences, Hefei National Laboratory, Shanghai 201315, China
  • 4Shanghai Xun Tai Quantech Co., Ltd., Shanghai 200241, China
  • show less
    DOI: 10.1364/PRJ.506960 Cite this Article Set citation alerts
    Lang Li, Minglu Cai, Tao Wang, Zicong Tan, Peng Huang, Kan Wu, Guihua Zeng, "On-chip source-device-independent quantum random number generator," Photonics Res. 12, 1379 (2024) Copy Citation Text show less
    Schematic diagram of the integrated SDI-QRNG on SiPh PIC. GC, grating coupler; PM, phase modulator; Att, attenuator; MMI, multimode interference splitter; AWG, arbitrary waveform generator; PD, photodetector; DSO, digital signal oscilloscope. The input state is the vacuum state, and the laser is used for quadrature component measurement.
    Fig. 1. Schematic diagram of the integrated SDI-QRNG on SiPh PIC. GC, grating coupler; PM, phase modulator; Att, attenuator; MMI, multimode interference splitter; AWG, arbitrary waveform generator; PD, photodetector; DSO, digital signal oscilloscope. The input state is the vacuum state, and the laser is used for quadrature component measurement.
    Schematic diagram of the signal processing flow of the on-chip SDI-QRNG system based on vacuum state. (a) Generation structure of secure random bits. (b) Measurement basis switching control modulation voltage signal for secure entropy estimation. When a switching control signal pulse occurs for selecting the measurement basis of the check quadrature Q^ (gray points), check data are obtained and used to estimate a bound on the practical on-chip quantum entropy Hminpra(Pδp|E) that determines how much remaining entropy of raw random number bits is secure. And raw numbers are secure by applying a strong randomness extractor calibrated Hminpra(Pδp|E) according to the protocol described before. Part of the secure random bits generated by the on-chip SDI-QRNG system are fed back to enhance the randomness of the measurement basis selection.
    Fig. 2. Schematic diagram of the signal processing flow of the on-chip SDI-QRNG system based on vacuum state. (a) Generation structure of secure random bits. (b) Measurement basis switching control modulation voltage signal for secure entropy estimation. When a switching control signal pulse occurs for selecting the measurement basis of the check quadrature Q^ (gray points), check data are obtained and used to estimate a bound on the practical on-chip quantum entropy Hminpra(Pδp|E) that determines how much remaining entropy of raw random number bits is secure. And raw numbers are secure by applying a strong randomness extractor calibrated Hminpra(Pδp|E) according to the protocol described before. Part of the secure random bits generated by the on-chip SDI-QRNG system are fed back to enhance the randomness of the measurement basis selection.
    (a) Experimental setup to characterize the bandwidth of the photodetector. Electro-optic S21 3 dB bandwidth of the (b) chip with DC gold wire package and (c) bare chip without package.
    Fig. 3. (a) Experimental setup to characterize the bandwidth of the photodetector. Electro-optic S21 3 dB bandwidth of the (b) chip with DC gold wire package and (c) bare chip without package.
    Source-device-independent chip on SiPh PIC. (a) An overall microscopic view of the SDI-QRNG chip, including grating couplers (GCs), the phase modulator (PM), the attenuator (Att), and photodetectors (PDs). This overall microscopic view shows the schematic diagram of the SDI-GRNG chip for the experiment. 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 Qδq. 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. (b) Micrograph view of the photodetector. This micrograph view shows that the PDs are implemented with a size of 16 μm×23 μm for light detection based on Ge PIN PD.
    Fig. 4. Source-device-independent chip on SiPh PIC. (a) An overall microscopic view of the SDI-QRNG chip, including grating couplers (GCs), the phase modulator (PM), the attenuator (Att), and photodetectors (PDs). This overall microscopic view shows the schematic diagram of the SDI-GRNG chip for the experiment. 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 Qδq. 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. (b) Micrograph view of the photodetector. This micrograph view shows that the PDs are implemented with a size of 16  μm×23  μm for light detection based on Ge PIN PD.
    Experimental homodyne measurement of the vacuum state on SiPh SDI-QRNG PIC. (a) The quadratures P and Q of the shot noise in each frame. (b) The switch driving signal on the PM.
    Fig. 5. Experimental homodyne measurement of the vacuum state on SiPh SDI-QRNG PIC. (a) The quadratures P and Q of the shot noise in each frame. (b) The switch driving signal on the PM.
    The quantum conditional min-entropy of each sample under 250 kHz basis switching. Hlow(Pδ|E) represents the quantum conditional min-entropy of each raw sample under 250 kHz basis switching, and Hlowϵ(Pδ10|E) represents the quantum conditional min-entropy of each raw sample under 250 kHz considering the finite-size effect.
    Fig. 6. The quantum conditional min-entropy of each sample under 250 kHz basis switching. Hlow(Pδ|E) represents the quantum conditional min-entropy of each raw sample under 250 kHz basis switching, and Hlowϵ(Pδ10|E) represents the quantum conditional min-entropy of each raw sample under 250 kHz considering the finite-size effect.
    Source-device-independent chip on SiPh PIC. (a) Photo of SDI-QRNG chip LAB device on a gas floating chip testing platform (packaged by wire bonding). The green PCB board inside is arranged neatly with gold wires to guide electrical signals for subsequent processing. (b) High-definition electron microscope image of photoelectric integration of the hybrid integrated package SDI-QRNG chip system. (c) Cross-sectional view of the photodetector.
    Fig. 7. Source-device-independent chip on SiPh PIC. (a) Photo of SDI-QRNG chip LAB device on a gas floating chip testing platform (packaged by wire bonding). The green PCB board inside is arranged neatly with gold wires to guide electrical signals for subsequent processing. (b) High-definition electron microscope image of photoelectric integration of the hybrid integrated package SDI-QRNG chip system. (c) Cross-sectional view of the photodetector.
    (a) The structure of grating coupler. (b) The coupling loss of fiber to the waveguide at the C band. The grating period is 630 nm with a duty ratio of 50%, and the shallow etching depth of the grating region is 70 nm. The operating wavelength of the grating coupler is 1550 nm, and the coupling loss is about 4 dB per facet. The fiber to waveguide 1 dB bandwidth is about 29.5 nm.
    Fig. 8. (a) The structure of grating coupler. (b) The coupling loss of fiber to the waveguide at the C band. The grating period is 630 nm with a duty ratio of 50%, and the shallow etching depth of the grating region is 70 nm. The operating wavelength of the grating coupler is 1550 nm, and the coupling loss is about 4 dB per facet. The fiber to waveguide 1 dB bandwidth is about 29.5 nm.
    (a) A cross-sectional view of the thermal phase shifter. (b) The test results of the extinction ratio versus the voltage of the thermal phase shifter. The thermal phase shifter used in the experiment is achieved by depositing a TiN layer. The height of the TiN heater is 120 nm, and the resistance is about 10–12 Ω/square. The phase shifting efficiency can be improved by the fabrication of the heat shield to reduce heat dissipation, with a dry etch 120 μm Si substrate. By adjusting the DC voltage applied to the re-attenuator, the amount of optical power input to the PD can be controlled on chip.
    Fig. 9. (a) A cross-sectional view of the thermal phase shifter. (b) The test results of the extinction ratio versus the voltage of the thermal phase shifter. The thermal phase shifter used in the experiment is achieved by depositing a TiN layer. The height of the TiN heater is 120 nm, and the resistance is about 10–12 Ω/square. The phase shifting efficiency can be improved by the fabrication of the heat shield to reduce heat dissipation, with a dry etch 120 μm Si substrate. By adjusting the DC voltage applied to the re-attenuator, the amount of optical power input to the PD can be controlled on chip.
    (a) Micrograph of a 2×2 50:50 multi-mode interference (MMI) splitter. (b) Response time of the photodetector. The insertion loss of the 2×2 50:50 MMI splitter is 0.5 dB, and the imbalance is about 5%. And the measured response time of the PD is about 345 ns, as shown above. The delay time is tested on a chip with a DC gold wire package.
    Fig. 10. (a) Micrograph of a 2×2 50:50 multi-mode interference (MMI) splitter. (b) Response time of the photodetector. The insertion loss of the 2×2 50:50 MMI splitter is 0.5 dB, and the imbalance is about 5%. And the measured response time of the PD is about 345 ns, as shown above. The delay time is tested on a chip with a DC gold wire package.
    (a) A cross-sectional view of the phase modulator. (b) Halfwave voltage of the phase modulator. The halfwave voltage of the PM has been measured with a triangular voltage sweep to verify the performance of the modulator. A 1 MHz triangular wave signal produced by the AWG was input into the modulator and the oscilloscope at the same time. The modulated signal is received by a photodetector with 1 GHz 3 dB bandwidth and subsequently loaded to the oscilloscope. As shown above, the blue line shows the received signal, and the red line shows the driving voltage.
    Fig. 11. (a) A cross-sectional view of the phase modulator. (b) Halfwave voltage of the phase modulator. The halfwave voltage of the PM has been measured with a triangular voltage sweep to verify the performance of the modulator. A 1 MHz triangular wave signal produced by the AWG was input into the modulator and the oscilloscope at the same time. The modulated signal is received by a photodetector with 1 GHz 3 dB bandwidth and subsequently loaded to the oscilloscope. As shown above, the blue line shows the received signal, and the red line shows the driving voltage.
    (a) The experiment setup of the on-chip SDI-QRNG detector linearity. (b) The on-chip SDI-QRNG detector linearity experimental test result. As shown above, the light source is a 1550 nm laser, and an attenuator for adjusting optical power is connected behind it. The light is illuminated to the PD surface by the on-chip vertical coupler. The photocurrent generated by the PD is separated into DC and AC signals through the bias-tee, and the DC signal is measured by the precision measure unit (Keysight B2901A). The experimental data points are fitted with linear curves, and the calculated responsivity is about 0.8 A/W. What is marked in the red star is the input optical power value commonly used in QRNG experiments. Due to the limitation of the maximum input optical power under experimental conditions, no obvious saturation phenomenon has been observed, so it can be considered that the detector has excellent linearity in the working area.
    Fig. 12. (a) The experiment setup of the on-chip SDI-QRNG detector linearity. (b) The on-chip SDI-QRNG detector linearity experimental test result. As shown above, the light source is a 1550 nm laser, and an attenuator for adjusting optical power is connected behind it. The light is illuminated to the PD surface by the on-chip vertical coupler. The photocurrent generated by the PD is separated into DC and AC signals through the bias-tee, and the DC signal is measured by the precision measure unit (Keysight B2901A). The experimental data points are fitted with linear curves, and the calculated responsivity is about 0.8 A/W. What is marked in the red star is the input optical power value commonly used in QRNG experiments. Due to the limitation of the maximum input optical power under experimental conditions, no obvious saturation phenomenon has been observed, so it can be considered that the detector has excellent linearity in the working area.
    (a) The quantum conditional min-entropy versus the minimum resolution of the quadrature data when the input is vacuum state; Hlow(Pδ‖E) coincides with Hinf(Pδ). (b) The quantum conditional min-entropy versus the minimum resolution of the quadrature data when the input is thermal state.
    Fig. 13. (a) The quantum conditional min-entropy versus the minimum resolution of the quadrature data when the input is vacuum state; Hlow(PδE) coincides with Hinf(Pδ). (b) The quantum conditional min-entropy versus the minimum resolution of the quadrature data when the input is thermal state.
    Experimental data. (a) The raw data distribution of the quadrature P of the shot noise. (b) The raw data distribution of the quadrature P of electronic noise. For 50 frames of data collected continuously, through offline data processing and monitoring, we ensure that the variance of the shot noise of each frame of data is greater than the variance of the electrical noise (to finally extract the secure random bits that eliminate the classical side channel information), and we can find that the raw data of the quadrature component P of the shot noise and electrical noise shown above have a good Gaussian property.
    Fig. 14. Experimental data. (a) The raw data distribution of the quadrature P of the shot noise. (b) The raw data distribution of the quadrature P of electronic noise. For 50 frames of data collected continuously, through offline data processing and monitoring, we ensure that the variance of the shot noise of each frame of data is greater than the variance of the electrical noise (to finally extract the secure random bits that eliminate the classical side channel information), and we can find that the raw data of the quadrature component P of the shot noise and electrical noise shown above have a good Gaussian property.
    Auto-correlation of original quadrature-P of shot noise. The result shows that the original data have almost no auto-correlation characteristics.
    Fig. 15. Auto-correlation of original quadrature-P of shot noise. The result shows that the original data have almost no auto-correlation characteristics.
    The quantum conditional min-entropy of each sample under 100 kHz basis switching. Hlow(Pδ|E) represents the quantum conditional min-entropy of each raw sample under 100 kHz basis switching, and Hlowϵ(Pδ10|E) represents the quantum conditional min-entropy of each raw sample under 100 kHz considering the finite-size effect.
    Fig. 16. The quantum conditional min-entropy of each sample under 100 kHz basis switching. Hlow(Pδ|E) represents the quantum conditional min-entropy of each raw sample under 100 kHz basis switching, and Hlowϵ(Pδ10|E) represents the quantum conditional min-entropy of each raw sample under 100 kHz considering the finite-size effect.
    Schematic diagram of the Toeplitz-hashing extractor. The goal of the Toeplitz-hashing extractor is to extract the secure random bits from the experiment raw random bits by establishing the Toeplitz matrix.
    Fig. 17. Schematic diagram of the Toeplitz-hashing extractor. The goal of the Toeplitz-hashing extractor is to extract the secure random bits from the experiment raw random bits by establishing the Toeplitz matrix.
    P-values of the 15 kinds of statistical tests for the extracted random bits. The NIST test suites contain a total of 15 statistical tests. Each test corresponds to a P-value. If the P-value is in the range of 0.0001 and 0.99, the test is considered to be passed. The blue bars represent the P-values of sub-tests for each statistical test. The red line indicates the pass criteria recommended by NIST due to all the P-values exceeding the typical threshold of 0.0001 [45,46].
    Fig. 18. P-values of the 15 kinds of statistical tests for the extracted random bits. The NIST test suites contain a total of 15 statistical tests. Each test corresponds to a P-value. If the P-value is in the range of 0.0001 and 0.99, the test is considered to be passed. The blue bars represent the P-values of sub-tests for each statistical test. The red line indicates the pass criteria recommended by NIST due to all the P-values exceeding the typical threshold of 0.0001 [45,46].
    Proportion of the 15 kinds of statistical tests for the extracted random bits. The NIST test suites contain a total of 15 statistical tests. All the extracted random bits in our experiment pass the NIST test due to all the pass proportions exceeding 0.98 [46].
    Fig. 19. Proportion of the 15 kinds of statistical tests for the extracted random bits. The NIST test suites contain a total of 15 statistical tests. All the extracted random bits in our experiment pass the NIST test due to all the pass proportions exceeding 0.98 [46].
    Lang Li, Minglu Cai, Tao Wang, Zicong Tan, Peng Huang, Kan Wu, Guihua Zeng, "On-chip source-device-independent quantum random number generator," Photonics Res. 12, 1379 (2024)
    Download Citation