Schmidt decomposition and multivariate statistical analysis

Yu. I. Bogdanov; N. A. Bogdanova; D. V. Fastovets; V. F. Luckichev

doi:10.1117/12.2266891

30 December 2016 Schmidt decomposition and multivariate statistical analysis

Yu. I. Bogdanov, N. A. Bogdanova, D. V. Fastovets, V. F. Luckichev

Proceedings Volume 10224, International Conference on Micro- and Nano-Electronics 2016; 102242P (2016) https://doi.org/10.1117/12.2266891
Event: The International Conference on Micro- and Nano-Electronics 2016, 2016, Zvenigorod, Russian Federation

Abstract

The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical correlation analysis. Correlation of photons in the beam splitter output channels, when input photons statistics is given by compound Poisson distribution is examined. The developed formalism allows us to analyze multidimensional systems and we have obtained analytical formulas for Schmidt decomposition of multivariate Gaussian states. It is shown that mathematical tools of quantum mechanics can significantly improve the classical statistical analysis. The presented formalism is the natural approach for the analysis of both classical and quantum multivariate systems and can be applied in various tasks associated with research of dependences.

Citation Download Citation

Yu. I. Bogdanov, N. A. Bogdanova, D. V. Fastovets, and V. F. Luckichev "Schmidt decomposition and multivariate statistical analysis", Proc. SPIE 10224, International Conference on Micro- and Nano-Electronics 2016, 102242P (30 December 2016); https://doi.org/10.1117/12.2266891

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