Schmidt decomposition and analysis of statistical correlations
- Authors: Bogdanov Y.I.1,2,3, Bogdanova N.A.1,2, Lukichev V.F.1, Fastovets D.V.1,2, Chernyavskii A.Y.1,4
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Affiliations:
- Institute of Physics and Technology
- National Research University of Electronic Technology MIET
- Moscow National Research Nuclear University MEPhI
- Moscow State University
- Issue: Vol 45, No 5 (2016)
- Pages: 314-323
- Section: Article
- URL: https://journals.rcsi.science/1063-7397/article/view/185729
- DOI: https://doi.org/10.1134/S1063739716050036
- ID: 185729
Cite item
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.
About the authors
Yu. I. Bogdanov
Institute of Physics and Technology; National Research University of Electronic Technology MIET; Moscow National Research Nuclear University MEPhI
Email: fast93@mail.ru
Russian Federation, Moscow; Moscow; Moscow
N. A. Bogdanova
Institute of Physics and Technology; National Research University of Electronic Technology MIET
Email: fast93@mail.ru
Russian Federation, Moscow; Moscow
V. F. Lukichev
Institute of Physics and Technology
Email: fast93@mail.ru
Russian Federation, Moscow
D. V. Fastovets
Institute of Physics and Technology; National Research University of Electronic Technology MIET
Author for correspondence.
Email: fast93@mail.ru
Russian Federation, Moscow; Moscow
A. Yu. Chernyavskii
Institute of Physics and Technology; Moscow State University
Email: fast93@mail.ru
Russian Federation, Moscow; Moscow