Entropy estimation in a spin-1 Bose-Einstein condensate

TL;DR

This paper explores how measurement distributions in a spin-1 Bose-Einstein condensate reveal quantum entropies and area laws, providing methods to estimate entropic quantities from finite data samples.

Contribution

It demonstrates that classical entropies and mutual informations in a spin-1 BEC reflect quantum entropic features like the area law, even in complex regimes, and introduces practical estimators for experimental data.

Findings

Classical entropies exhibit the area law in a spin-1 BEC.

Mutual information captures quantum correlations.

Finite-sample estimators enable experimental measurement.

Abstract

We investigate the information extractable from measurement distributions of two non-commuting spin observables in a multi-well spin-1 Bose-Einstein condensate. We provide a variety of analytic and numerical evidence that suitably chosen classical entropies and classical mutual informations thereof contain the typical feature of quantum entropies known in quantum field theories, that is, the area law, even in the non-Gaussian regime and for a non-zero temperature. Towards a feasible experimental implementation, we estimate entropic quantities from a finite number of samples without any additional assumptions on the underlying quantum state using k-nearest neighbor estimators.