# Entanglement in spinor Bose gases via entropic uncertainty relations

### Abstract

We develop a theoretical framework to witness entanglement in spinor Bose gases using entropic uncertainty relations. Simultaneous measurements of two non-commuting spin observables (here $S_x$ and $Q_{yz}$) allows for direct access to a quasi-probability distribution [Fig. 1(b)] and its associated entropy. In the Gaussian regime this corresponds to the Husimi distribution and Wehrl entropy, respectively. We simulate the system via the truncated Wigner approximation and perform a covariance analysis of the distribution [Fig. 1(c)]. We observe a non-zero Wehrl mutual information $I_W$ [Fig. 1(d)], where $I_W > 0$ is a perfect entanglement witness as it measures only the quantum correlations (given the initial state has zero classical correlations). Future work will extend the analysis to the non-Gaussian regime to understand the long-time behaviour of entanglement.

Date
May 26, 2021 — May 28, 2021
Location
Online (due to COVID)
##### Oliver Stockdale
###### PhD student in Physics

My research interests include ultracold quantum gases, entanglement detection, entropic uncertainty relations, and superfluidity