Entanglement quantification in atomic ensembles

TL;DR

This paper develops a practical method to quantify entanglement in atomic ensembles using variance-based criteria, enabling entanglement measurement with limited experimental data, demonstrated on spin-squeezed Bose-Einstein condensates.

Contribution

It derives analytical lower bounds for entanglement measures based on variances, facilitating entanglement quantification with minimal measurements in realistic experiments.

Findings

Successfully quantified bipartite and multipartite entanglement in Bose-Einstein condensates.

Provided a practical approach for entanglement measurement with only first and second moments.

Demonstrated the method's effectiveness on systems with around 500 atoms.

Abstract

Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement criteria that are based on variances of arbitrary operators and analytically derive the lower bounds these criteria provide for two relevant entanglement measures: the best separable approximation (BSA) and the generalized robustness (GR). This yields a practical method for quantifying entanglement in realistic experimental situations, in particular, when only few measurements of simple observables are available. As a concrete application of this method, we quantify bipartite and multipartite entanglement in spin-squeezed Bose-Einstein condensates of $\sim 500$ atoms, by lower bounding the BSA and the GR only from measurements of first and second moments of the collective spin operator.