[1] C. E. Shannon. Communication theory of secrecy systems. Bell Syst. Tech. J., 28, 656-715(1949).

[2] N. Metropolis, S. Ulam. The Monte Carlo method. J. Am. Stat. Assoc., 44, 335-341(1949).

[3] W. Schindler, W. Killmann. Evaluation criteria for true (physical) random number generators used in cryptographic applications. Cryptographic Hardware and Embedded Systems (CHES), 431-449(2002).

[4] W. T. Holman, J. A. Connelly, A. B. Dowlatabadi. An integrated analog/digital random noise source. IEE Trans. Circuits Syst. I, 44, 521-528(1997).

[5] M. Bucci, L. Germani, R. Luzzi. A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC. IEEE Trans. Comput., 52, 403-409(2003).

[6] C. Tokunaga, D. Blaauw, T. Mudge. True random number generator with a metastability-based quality control. IEEE J. Solid-State Circuits, 43, 78-85(2008).

[7] J. F. Dynes, Z. L. Yuan, A. W. Sharpe. A high speed, postprocessing free, quantum random number generator. Appl. Phys. Lett., 93, 031109(2008).

[8] M. A. Wayne, P. G. Kwiat. Low-bias high-speed quantum random number generator via shaped optical pulses. Opt. Express, 18, 9351-9357(2010).

[9] H. Fürst, H. Weier, S. Nauerth. High speed optical quantum random number generation. Opt. Express, 18, 13029-13037(2010).

[10] C. Gabriel, C. Wittmann, D. Sych. A generator for unique quantum random numbers based on vacuum states. Nat. Photonics, 4, 711-715(2010).

[11] Y.-Y. Hu, Y.-Y. Ding, S. Wang. Compact quantum random number generation using a linear optocoupler. Opt. Lett., 46, 3175-3178(2021).

[12] E. Pelucchi, G. Fagas, I. Aharonovich. The potential and global outlook of integrated photonics for quantum technologies. Nat. Rev. Phys., 4, 194-208(2022).

[13] J. Wang, F. Sciarrino, A. Laing. Integrated photonic quantum technologies. Nat. Photonics, 14, 273-284(2020).

[14] G. Zhang, J. Y. Haw, H. Cai. An integrated silicon photonic chip platform for continuous-variable quantum key distribution. Nat. Photonics, 13, 839-842(2019).

[15] C. Abellan, W. Amaya, D. Domenech. Quantum entropy source on an InP photonic integrated circuit for random number generation. Optica, 3, 989-994(2016).

[16] B. Bai, J. Huang, G.-R. Qiao. 18.8 Gbps real-time quantum random number generator with a photonic integrated chip. Appl. Phys. Lett., 118, 264001(2021).

[17] F. Raffaelli, P. Sibson, J. E. Kennard. Generation of random numbers by measuring phase fluctuations from a laser diode with a silicon-on-insulator chip. Opt. Express, 26, 19730-19741(2018).

[18] F. Raffaelli, P. Sibson, J. E. Kennard. A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers. Quantum Sci. Technol., 3, 025003(2018).

[19] F. Raffaelli, P. Sibson, J. E. Kennard. Multiplexed quantum random number generation. Quantum, 3, 141(2019).

[20] C. Bruynsteen, T. Gehring, C. Lupo. 100-Gbit/s integrated quantum random number generator based on vacuum fluctuations. PRX Quantum, 4, 010330(2023).

[21] Z. Cao, H. Zhou, X. Yuan. Source-independent quantum random number generation. Phys. Rev. X, 6, 011020(2016).

[22] D. G. Marangon, G. Vallone, P. Villoresi. Source-device-independent ultrafast quantum random number generation. Phys. Rev. Lett., 18, 060503(2017).

[23] T. Michel, J. Y. Haw, D. G. Marangon. Real-time source-independent quantum random-number generator with squeezed states. Phys. Rev. Appl., 12, 034017(2019).

[24] X. Lin, R. Wang, S. Wang. Imperfection-insensitivity quantum random number generator with untrusted daily illumination. Opt. Express, 30, 25474-25485(2022).

[25] S. Pironio. Random numbers certified by Bell’s theorem. Nature, 464, 1021-1024(2010).

[26] R. Colbeck, R. Renner. Free randomness can be amplified. Nat. Phys., 8, 450-453(2012).

[27] R. Gallego, L. Masanes, G. De La Torre. Full randomness from arbitrarily deterministic events. Nat. Commun., 4, 2654(2013).

[28] B. G. Christensen, K. T. McCusker, J. B. Altepeter. Detection-loophole-free test of quantum nonlocality, and applications. Phys. Rev. Lett., 111, 130406(2013).

[29] B. Hensen. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526, 682-686(2015).

[30] M. Giustina, M. A. M. Versteegh, S. Wengerowsky. Significant-loophole-free test of Bell’s theorem with entangled photons. Phys. Rev. Lett., 115, 250401(2015).

[31] L. K. Shalm, E. Meyer-Scott, B. G. Christensen. Strong loophole-free test of local realism. Phys. Rev. Lett., 115, 250402(2015).

[32] W. Rosenfeld, D. Burchardt, R. Garthoff. Event-ready Bell test using entangled atoms simultaneously closing detection and locality loopholes. Phys. Rev. Lett., 119, 010402(2017).

[33] X. Lin, S. Wang, Z.-Q. Yin. Security analysis and improvement of source independent quantum random number generators with imperfect devices. npj Quantum Inf., 6, 100(2020).

[34] X. Lin, R. Wang, S. Wang. Certified randomness from untrusted sources and uncharacterized measurements. Phys. Rev. Lett., 129, 050506(2022).

[35] J. N. Zhang, R. Yang, X. Li. Realization of a source-device-independent quantum random number generator secured by nonlocal dispersion cancellation. Adv. Photonics, 5, 036003(2023).

[36] D. Drahi, N. Walk, M. J. Hoban. Certified quantum random numbers from untrusted light. Phys. Rev. X, 10, 041048(2020).

[37] Y. H. Li, X. Han, Y. Cao. Quantum random number generation with uncharacterized laser and sunlight. npj Quantum Inf., 5, 97(2019).

[38] M. Pivoluska, M. Plesch, M. Farkas. Semi-device-independent random number generation with flexible assumptions. npj Quantum Inf., 7, 50(2021).

[39] Y. Zhang, H. P. Lo, A. Mink. A simple low-latency real-time certifiable quantum random number generator. Nat. Commun., 12, 1056(2021).

[40] M. Avesani, D. G. Marangon, G. Vallone. Source-device-independent heterodyne-based quantum random number generator at 17 Gbps. Nat. Commun., 9, 5365(2018).

[41] M. Herrero-Collantes, J. C. EscartinGarcia-. Quantum random number generators. Rev. Mod. Phys., 89, 015004(2017).

[42] F. Laudenbach, C. Pacher, C. H. F. Fung. Continuous-variable quantum key distribution with gaussian modulation -- the theory of practical implementations. Adv. Quantum Technol., 1, 1800011(2018).

[43] L. Li, P. Huang, T. Wang. Practical security of a chip-based continuous-variable quantum-key-distribution system. Phys. Rev. A, 103, 032611(2021).

[44] P. Ye, W. Chen, Z.-H. Wang. Transmittance-invariant phase modulator for chip-based quantum key distribution. Opt. Express, 30, 39911-39921(2022).

[45] P. R. Smith, D. G. Marangon, M. Lucamarini. Simple source device-independent continuous-variable quantum random number generator. Phys. Rev. A, 99, 062326(2019).

[46] K. Kim, S. Bittner, Y. Zeng. Massively parallel ultrafast random bit generation with a chip-scale laser. Science, 371, 948-952(2021).

[47] A. Uchida, K. Amano, M. Inoue. Fast physical random bit generation with chaotic semiconductor lasers. Nat. Photonics, 2, 728-732(2008).

[48] C. R. S. Williams, J. C. Salevan, X. Li. Fast physical random number generator using amplified spontaneous emission. Opt. Express, 18, 23584-23597(2010).

[49] B. Barak, R. Shaltiel, E. Tromer. True random number generators secure in a changing environment. Cryptographic Hardware and Embedded Systems (CHES), 166-180(2003).

[50] X. Ma, F. Xu, H. Xu. Postprocessing for quantum random-number generators: entropy evaluation and randomness extraction. Phys. Rev. A, 87, 062327(2013).

[51] P. J. Bustard, D. G. England, J. Nunn. Quantum random bit generation using energy fluctuations in stimulated Raman scattering. Opt. Express, 21, 29350-29357(2013).

[52] B. Barak, Y. Dodis, H. Krawczyk. Leftover hash lemma, revisited. Advances in Cryptology-CRYPTO, 1-20(2011).

[53] F. Xu, B. Qi, X. Ma. Ultrafast quantum random number generation based on quantum phase fluctuations. Opt. Express, 20, 12366-12377(2012).