Correlation defense for quantum randomness

N.S. Perminova,b , O.I. Bannika , D.U. Tarankovaa , R.R. Nigmatullina

aKazan National Research Technical University named after A.N. Tupolev, Kazan, 420111 Russia

bZavoisky Physical-Technical Institute, FRC Kazan Scientific Center, Russian Academy of Sciences, Kazan, 420029 Russia

Full text pdf

DOI: 10.26907/2541-7746.2020.1.98-106

For citation: Perminov N.S., Bannik O.I., Tarankova D.Yu., Nigmatullin R.R. Correlation defense for quantum randomness. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2020, vol. 162, no. 1, pp. 98–106. doi: 10.26907/2541-7746.2020.1.98-106.

Для цитирования: Perminov N.S., Bannik O.I., Tarankova D.Yu., Nigmatullin R.R. Correlation defense for quantum randomness // Учен. зап. Казан. ун-та. Сер. Физ.-матем. науки. – 2020. – Т. 162, кн. 1. – С. 98–106. – doi: 10.26907/2541-7746.2020.1.98-106.

Abstract

New nonparametric methods were developed for verification and monitoring of quantum randomness based on the ranged correlation function (RCF) and a sequence of the ranged amplitudes (SRA). RCF analysis of different topology subsamples from the raw data of the prototype of a quantum random number generator on homodyne detection was carried out. It was shown that in the real system there are weak local regression relations, for which it is possible to introduce a robust criterion of significance. Precise SRA identification of the long samples statistics was carried out. The obtained results extend the traditional entropy methods of the useful randomness analysis and open the way for creation of new strict quality quantum standards and defense for physical random number generators.

Keywords: quantum information, ranged correlation functions, RCF defense, quantum randomness, physical random number generator

Acknowledgments. The research of noise in the area of photonics and quantum technologies was funded by the Government of the Russian Federation (project no. 14.Z50.31.0040; Feb. 17, 2017 (experimental part)). The work was also supported in part by the grant for young scientists of the Republic of Tatarstan (project no. 06-36-ts-G 2018 (theoretical part)).

References

  1. Pusey M.F., Barrett J., Rudolph T. On the reality of the quantum state. Nat. Phys., 2012, vol. 8, no. 6, pp. 475–478. doi: 10.1038/nphys2309.
  2. Paterek T., Kofler J., Prevedel R., Klimek P., Aspelmeyer M., Zeilinger A., Brukner Cˇ . Logical independence and quantum randomness. New J. Phys., 2010, vol. 12, no. 1, art. 013019, pp. 1–9. doi: 10.1088/1367-2630/12/1/013019.
  3. Nigmatullin R.R., Evdokimov Yu.K., Denisov E.S., Zhang W. New methods of complex systems inspection: Comparison of the ADC device in different operating modes. In: Computational Problems in Science and Engineering. Springer, 2015, pp. 187–204, doi: 10.1007/978-3-319-15765-8_9.
  4. Smirnov M.A., Perminov N.S., Nigmatullin R.R., Talipov A.A., Moiseev S.A. Sequences of the ranged amplitudes as a universal method for fast noninvasive characterization of SPAD dark counts. Appl. Opt., 2018, vol. 57, no. 1, pp. 57–61. doi: 10.1364/AO.57.000057.
  5. Perminov N.S., Smirnov M.A., Nigmatullin R.R., Talipov A.A., Moiseev S.A. Comparison of the capabilities of histograms and a method of ranged amplitudes in noise analysis of single-photon detectors. Comput. Opt., 2018, vol. 42, no. 2, pp. 338–342. doi: 10.18287/2412-6179-2018-42-2-338-342.
  6. Gisin N., Ribordy G., Tittel W., Zbinden H. Quantum cryptography. Rev. Mod. Phys., 2002, vol. 74, no. 1, pp. 145–195. doi: 10.1103/RevModPhys.74.145.
  7. Balygin K.A., Zaitsev V.I., Klimov A.N., Kulik S.P., Molotkov S.N. Implementation of a quantum random number generator based on the optimal clustering of photocounts. JETP Lett., 2017, vol. 106, no. 7, pp. 470–476. doi: 10.1134/S0021364017190043.
  8. Gabriel C., Wittmann C., Sysh D., Dong R., Mauerer W., Anderson U.L., Marquardt C., Leuchs G. A generator for unique quantum random numbers based on vacuum states. Nat. Photonics, 2010, vol. 4, pp. 711–715. doi: 10.1038/nphoton.2010.197.
  9. Box G.F., Jenkins G.M., Reinsel G.C., Ljung G.M. Time Series Analysis: Forecasting and Control. Wiley & Sons, 2015. 712 p.
  10. Nigmatullin R.R. The statistics of the fractional moments: Is there any chance to “read quantitatively” any randomness? Comput. Probl. Sci. Eng. Signal Process., 2006, vol. 86, no. 10, pp. 2529–2547. doi: 10.1016/j.sigpro.2006.02.003.
  11. Stephens M.A. Introduction to Kolmogorov (1933) on the empirical determination of a distribution. In: Breakthroughs in Statistics. New York, Springer, 1992, pp. 93–105. doi: 10.1007/978-1-4612-4380-9_9.
  12. Kamps U. A concept of generalized order statistics. J. Stat. Plann., 1995, vol. 48, no. 1, pp. 1–23. doi: 10.1016/0378-3758(94)00147-N.
  13. Heckert A., Dray J., Vo S., Rukhin A., Soto J., Nechvatal J., Smid M., Barker E., Leigh S., Levenson M., Vangel M., Banks D. A statistical test suite for random and pseudorandom number generators for cryptographic applications. Special Publication (NIST SP), Rep. 800-22 Rev 1a.
  14. Spitsyn V.G., Bolotova Yu.A., Phan N.H., Bui T.T.T. Using a haar wavelet transform, principal component analysis and neural networks for OCR in the presence of impulse noise. Comput. Opt., 2016, vol. 40, no. 2, pp. 249–257. doi: 10.18287/2412-6179-2016-40-2-249-257.
  15. Umnov A.V., Krylov A.S. Research of sparse representation method for ringing suppression. Comput. Opt., 2016, vol. 40, no. 6, pp. 895–903. doi: 10.18287/2412-6179-2016-40-6-895-903.
  16. Latypov R.Kh., Stolov E.L. Theory of ternary jitter-based true random number generators composed of identical gates. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 2, pp. 246–262.
  17. Nigmatullin R.R. Nanonoise: New non-invasive methods to read random sequences quantitatively. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2007, vol. 149, no. 3, pp. 71–83.

 

The content is available under the license Creative Commons Attribution 4.0 License.