Geodesic
Mathematical model of random number generator based on vacuum fluctuations
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 2, pp. 136-153 Cet article a éte moissonné depuis la source Math-Net.Ru

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A mathematical model of quantum random number generator based on vacuum fluctuations is considered. A mathematical justification for the "randomness’’ of the generated sequence is given under the assumption of the truth of the basic postulates of quantum theory and the validity of the Poisson probability distribution for the photon flux. The results of experiments and the obtained estimates of the minimum entropy are presented.
Keywords: quantum random number generator, minimal entropy estimation, vacuum fluctuations. 
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A. A. Gaidash; R. K. Goncharov; A. V. Kozubov; P. V. Yakovlev. Mathematical model of random number generator based on vacuum fluctuations. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 2, pp. 136-153. http://geodesic.mathdoc.fr/item/VSPUI_2024_20_2_a1/

[1] Ermakov S. M., Monte-Carlo method and related issues, Nauka Publ, M., 1975, 472 pp. (In Russian)

[2] Prokaev A. N., “The maximum entropy principle in search theory”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 19:1 (2023), 27–42 (In Russian) | DOI | MR

[3] Herrero-Collantes M., Garcia-Escartin J. C., “Quantum random number generators”, Rev. Mod. Phys., 89:2 (2017), 015004 | DOI | MR

[4] Gabriel C., Wittmann C., Sych D., Dong R., Mauerer W., Andersen U. L., Marquardt C., Leuchs G., “A generator for unique quantum random numbers based on vacuum states”, Nature Photon, 2010, no. 4, 711–715 | DOI

[5] Shi Y., Chng B., Kurtsiefer C., “Random numbers from vacuum fluctuations”, Applied Physics Letters, 109:4 (2016), 041101, 1–5 | DOI

[6] Bruynsteen C., Gehring T., Lupo C., Bauwelinck J., Yin X., “100-Gbit/s integrated quantum random number generator based on vacuum fluctuations”, PRX Quantum, 4:1 (2023), 010330 | DOI

[7] Gehring T., Lupo C., Kordts A., Solar N. D., Jain N., Rydberg T., Pedersen T. B., Pirandola S., Andersen U. L., “Homodyne-based quantum random number generator at 2.9 Gbps secure against quantum side-information”, Nature Communications, 12:1 (2021), 605 | DOI

[8] Drahi D., Walk N., Hoban M. J., Fedorov A. K., Shakhovoy R., Feimov A., Kurochkin Y., Kolthammer W. S., Nunn J., Barrett J., Walmsley I. A., “Certified quantum random numbers from untrusted light”, Physical Review X, 10:4 (2020), 041048, arXiv: 1905.09665 | DOI

[9] Schleich W. P., Quantum optics in phase space, Fizmatgiz Publ, M., 2005, 760 pp. (In Russian)

[10] Collett M. J., Loudon R., Gardiner C. W., “Quantum theory of optical homodyne and heterodyne detection”, Journal of Modern Optics, 34:6–7 (1987), 881–902 | DOI

[11] Tomamichel M., Schaffner C., Smith A., Renner R., “Leftover hashing against quantum side information”, IEEE Transactions on Information Theory, 57:8 (2011), 5524–5535 | DOI | MR | Zbl

[12] Carter J. L., Wegman M. N., “Universal classes of hash functions”, Journal of Computer and System Sciences, 18:2 (1979), 143–154 | DOI | MR | Zbl

[13] Mansour Y., Nisan N., Tiwari P., “The computational complexity of universal hashing”, Theoretical Computer Science, 107 (1993), 121–133 | DOI | MR | Zbl

[14] Ma X., Xu F., Xu H., Tan X., Qi B., Lo H.-K., “Postprocessing for quantum random-number generators: entropy evaluation and randomness extraction”, Physical Review A, 87:6 (2013) | DOI | MR

[15] Tikhonov V. I., Mironov M. A., Markov processes, Sov. Radio Publ, M., 1977, 488 pp. (In Russian) | MR

[16] Abramovitz M., Stegun I., Handbook of mathematical functions with formulas, graphs, and mathematical tables, Nauka Publ, M., 1979, 832 pp. (In Russian)

[17] Irwin J. O., “The frequency distribution of the difference between two independent variates following the same Poisson distribution”, Journal of the Royal Statistical Society. Series A, 100:3 (1937), 415–416 | DOI | Zbl

[18] Skellam J. G., “The frequency distribution of the difference between two Poisson variates belonging to different populations”, Journal of the Royal Statistical Society. Series A, 109:3 (1946), 290–296 | DOI | MR

[19] Vogel V., Grabow J., “Statistics of difference events in homodyne detection”, Physical Review A, 47:5 (1993), 4227–4235 | DOI

[20] Feller W., An introduction to probability theory and its applications, In 2 vol., v. 2, Mir Publ, M., 1984, 738 pp. (In Russian) | MR

[21] Haw J. Y., Assad S. M., Lance A. M., Ng N. H. Y., Sharma V., Lam P. K., Symul T., “Maximization of extractable randomness in a quantum random-number generator”, Physical Review Appl., 3:5 (2015), 054004 | DOI | MR

[22] Bendat J. S., Piersol A.G., Random data analysis and measurement procedures, Mir Publ, M., 1989, 540 pp. (In Russian)