Non-Gaussianity and purity in finite dimension

TL;DR

This paper investigates the statistical properties of truncated continuous variable states in finite-dimensional Hilbert spaces, focusing on purity and non-Gaussianity distributions up to dimension 21, and derives approximate formulas for their typical values.

Contribution

It provides a numerical analysis of purity and non-Gaussianity distributions in finite-dimensional systems and introduces approximate formulas for their typical values as functions of dimension.

Findings

Purity and non-Gaussianity are centered around typical values with decreasing variance as dimension increases.

Approximate formulas for typical purity and non-Gaussianity as functions of dimension are derived.

Distributions become more concentrated around the mean with increasing Hilbert space dimension.

Abstract

We address truncated states of continuous variable systems and analyze their statistical properties numerically by generating random states in finite-dimensional Hilbert spaces. In particular, we focus to the distribution of purity and non-Gaussianity for dimension up to d=21. We found that both quantities are distributed around typical values with variances that decrease for increasing dimension. Approximate formulas for typical purity and non-Gaussianity as a function of the dimension are derived.