Tensor rank problem in statistical high-dimensional data and quantum information theory:their comparisons on the methods and the results

TL;DR

This paper compares the use of tensor rank in quantum information theory and high-dimensional statistics, highlighting their similarities, differences, and the methods employed in each field.

Contribution

It demonstrates that quantum communication and statistical data analysis share common goals related to tensor rank and compares two specific methods used in each domain.

Findings

Range criterion method from quantum communication analyzed

Determinant polynomial method examined in statistical context

Both methods address tensor rank problems in high-dimensional data

Abstract

Quantum communication is concerned with the complexity of entanglement of a state and statistical data analysis is concerned with the complexity of a model. A common key word for both is "rank". In this paper we will show that both community is tracing the same target and that the methods used are slightly different. Two different methods, the range criterion method from quantum communication and the determinant polynomial method, are shown as an examples.