  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.

Quantum Physics