# From single-particle physical distributions to probabilistic measures of two-particle entanglement

## TL;DR

This paper develops an inversion method to infer two-particle entanglement information from measurable one-particle distributions in a one-dimensional quantum system, advancing the analysis of quantum correlations.

## Contribution

It introduces a novel inversion technique based on a shell-like expansion to extract entanglement data from one-particle distributions, tailored for a harmonically confined Heisenberg model.

## Key findings

- The method successfully relates one-particle distributions to entanglement measures.
- An approximate optimization scheme is proposed for various inter-particle interactions.
- The approach is grounded in exact mathematical constraints derived from the model.

## Abstract

An inversion method is formulated for extracting entanglement-related information on two-particle interactions in a one-dimensional system from measurable one-particle position- and momentum-distribution functions. The method is based on a shell-like expansion of these norm-1 measured quantities in terms of product states taken from a parametric orthonormal complete set. The mathematical constraints deduced from these point-wise expansions are restricted by the underlying physics of our harmonically confined and interacting Heisenberg model. Based on these exact results, we introduce an approximate optimization scheme for different inter-particle interactions and discuss it from the point of view of entropic correlation measures.