Extraction of quantum randomness

I.M. Arbekov^a, S.N. Molotkov^†^{a, b, c, d}
^aAcademy of Cryptography of the Russian Federation, PO Box 100, Moscow, 119331, Russian Federation
^bOsipyan Institute of Solid State Physics, Russian Academy of Sciences, Akademika Osip'yana str. 2, Chernogolovka, Moscow Region, 142432, Russian Federation
^cFaculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University, Leninskie Gory 1, build. 52, Moscow, 119991, Russian Federation
^dQuantum Technology Center of Lomonosov Moscow State University, Leninskie Gory 1, build. 35, Moscow, 119991, Russian Federation

The nature of randomness and constructive and provable methods to obtain (extract) it from observations of physical systems are discussed. True randomness, which exists only in a microcosm in the quantum-mechanical description of physical systems, is a fundamental property of quantum systems, which manifests itself in the outcomes of measurements upon quantum systems. The classical description of physical systems does not include any randomness and, in fact, it is introduced 'manually' by means of uncertainty — unknown initial conditions. Methods to really 'feel' quantum randomness are discussed using the example of a quantum device, a random number generator. Issues related to the 'proof' of randomness — testing of numerical sequences — are reviewed, and logical constructions that underlie such testing are analyzed. A mathematical apparatus is used to this end, which does not require special academic training, so standard knowledge from university courses on quantum mechanics and probability theory is sufficient. The authors aim to track a unified logical path from the origin of randomness in the quantum domain to its extraction, physical implementation, and testing.

Keywords: quantum random number generators, randomness extraction
PACS: 03.67.Dd, 42.50.Ex (all)
DOI: 10.3367/UFNe.2020.11.038890
URL: https://ufn.ru/en/articles/2021/6/d/
Web of Science

000691293300004
Scopus

2-s2.0-85114966083
ADS NASA

2021PhyU...64..617A
Citation: Arbekov I M, Molotkov S N "Extraction of quantum randomness" Phys. Usp. 64 617–634 (2021)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 15th, May 2020, revised: 28th, October 2020, accepted: 29th, November 2020

Оригинал: Арбеков И М, Молотков С Н «Об экстракции квантовой случайности» УФН 191 651–669 (2021); DOI: 10.3367/UFNr.2020.11.038890

References (27) ↓ Cited by (8) Similar articles (18)

Bennett C H, Brassard G Proc. of the IEEE Intern. Conf. on Computers, Systems, and Signal Processing, Bangalore, 10 - 12 December 1984 (Piscataway, NJ: IEEE, 1984) p. 175
Koç Ç K (Ed.) Cryptographic Engineering (New York: Springer, 2009)
Vasilenko V V Informatsionnye Voiny (3) 23 (2012)
Srinivasan S et al 2010 IEEE Symp. on VLSI Circuits, 16 - 18 June 2010, Honolulu, HI, USA (Piscataway, NJ: IEEE, 1984) p. 203
Galton F Natural Inheritance (London: Macmillan, 1894)
Herrero-Collantes M, Garcia-Escartin J C Rev. Mod. Phys. 89 015004 (2017)
Einstein A Ann. Physik 17 132 (1905)
Klyshko D N Fotony i Nelineinaya Optika (M.: Nauka, 1980); Per. na angl. yaz., Klyshko D N Photons And Nonlinear Optics (New York: Gordon and Breach, 1988)
Klyshko D N, Masalov A V Usp. Fiz. Nauk 165 1249 (1995); Klyshko D N, Masalov A V Phys. Usp. 38 1203 (1995)
Mandel L, Wolf E Optical Coherence And Quantum Optics (Cambridge: Cambridge Univ. Press, 1995); Per. na russk. yaz., Mandel’ E, Vol’f E Opticheskaya Kogerentnost’ i Kvantovaya Optika (M.: Fizmatlit, 2000)
Shannon C E Bell Syst. Tech. J. 27 379 (1948)
Shannon C E Bell Syst. Tech. J. 27 623 (1948)
Shennon K Raboty Po Teorii Informatsii i Kibernetike (M.: IL, 1963)
Cover T M, Thomas J A Elements Of Information Theory (New York: Wiley, 1991)
Molotkov S N Pis’ma ZhETF 105 374 (2017); Molotkov S N JETP Lett. 105 395 (2017)
Balygin K A i dr Zh. Eksp. Teor. Fiz. 153 879 (2018); Balygin K A et al J. Exp. Theor. Phys. 126 728 (2018)
Balygin K A et al Laser Phys. Lett. 14 125207 (2017)
Balygin K A i dr Pis’ma ZhETF 106 451 (2017); Balygin K A et al JETP Lett. 106 470 (2017)
Von Neumann J Applied Mathematics Series Vol. 12 (Washington, DC: U.S. National Bureau of Standards, 1951) p. 36; Reprinted in, Von Neumann J Neumann’s Collected Works Vol. 5 (Oxford: Pergamon Press, 1963) p. 768
Feller W An Introduction To Probability Theory And Its Applications 2nd ed. (New York: Wiley, 1957); Per. na russk. yaz., Feller V Vvedenie v Teoriyu Veroyatnostei i Ee Prilozheniya Vol. 1 (M.: Mir, 1964)
Babkin V F Problemy Peredachi Informatsii 7 (4) 13 (1971)
Buzhan P et al Nucl. Instrum. Meth. Phys. Res. A 567 78 (2006)
Kalashnikov D A, Tan S-H, Krivitsky L A Opt. Express 20 5044 (2012)
Computer Security esource Center, http://csrc.nist.gov/rng/SP800-22b.pdf
Knuth D E The Art Of Computer Programming Vol. 2 (Cambridge: Addison Wesley, 1981)
Marsaglia G http://stat.fsu.edu/pub/diehard
Cramer H Mathematical Methods Of Statistics (Princeton, NJ: Princeton Univ. Press, 1946)