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Schmidt decomposition and analysis of statistical correlations

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Abstract

The new correlation data analysis method based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. It is shown that mathematical methods of quantum mechanics allow us to develop new effective tools for the analysis of statistical dependences and relationships. The presented formalism is the natural approach for the analysis of both classical and quantum correlations. Algorithms of the calculation of partial and multiple correlation coefficients using Schmidt numbers were studied. Numerical estimates of these correlation coefficients were calculated for different probability distributions and quantum states.

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Authors and Affiliations

  1. Institute of Physics and Technology, Russian Academy of Sciences, Moscow, Russia

    Yu. I. Bogdanov, N. A. Bogdanova, V. F. Lukichev, D. V. Fastovets & A. Yu. Chernyavskii

  2. National Research University of Electronic Technology MIET, Moscow, Russia

    Yu. I. Bogdanov, N. A. Bogdanova & D. V. Fastovets

  3. Moscow National Research Nuclear University MEPhI, Moscow, Russia

    Yu. I. Bogdanov

  4. Moscow State University, Moscow, Russia

    A. Yu. Chernyavskii

Authors
  1. Yu. I. Bogdanov
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  2. N. A. Bogdanova
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  3. V. F. Lukichev
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  4. D. V. Fastovets
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  5. A. Yu. Chernyavskii
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Corresponding author

Correspondence to D. V. Fastovets.

Additional information

Original Russian Text © Yu.I. Bogdanov, N.A. Bogdanova, V.F. Lukichev, D.V. Fastovets, A.Yu. Chernyavskii, 2016, published in Mikroelektronika, 2016, Vol. 45, No. 5, pp. 342–351.

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Bogdanov, Y.I., Bogdanova, N.A., Lukichev, V.F. et al. Schmidt decomposition and analysis of statistical correlations. Russ Microelectron 45, 314–323 (2016). https://doi.org/10.1134/S1063739716050036

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  • DOI: https://doi.org/10.1134/S1063739716050036

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