Compressibility of positive semidefinite factorizations and quantum models

TL;DR

This paper explores how to compress positive semidefinite matrices and quantum models while approximately maintaining their inner products, with implications for data analysis and quantum communication complexity.

Contribution

It provides new bounds on the compressibility of positive semidefinite factorizations and quantum models, bridging matrix factorization and quantum information theory.

Findings

Derived bounds on compressibility of positive semidefinite matrices

Applicable to quantum models and data analysis

Impacts quantum communication complexity

Abstract

We investigate compressibility of the dimension of positive semidefinite matrices while approximately preserving their pairwise inner products. This can either be regarded as compression of positive semidefinite factorizations of nonnegative matrices or (if the matrices are subject to additional normalization constraints) as compression of quantum models. We derive both lower and upper bounds on compressibility. Applications are broad and range from the statistical analysis of experimental data to bounding the one-way quantum communication complexity of Boolean functions.