Schmidt decomposition and multivariate statistical analysis

TL;DR

This paper introduces a novel multivariate data analysis method using quantum-inspired Schmidt decomposition, enabling improved analysis of complex classical and quantum systems with analytical formulas for Gaussian states.

Contribution

It presents a new formalism applying quantum mechanical tools to classical statistical correlation analysis, including analytical formulas for Gaussian states.

Findings

Quantum-inspired formalism enhances classical statistical analysis.

Analytical formulas derived for multivariate Gaussian states.

Applicable to both classical and quantum multivariate systems.

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.