Wehrl entropy, entropic uncertainty relations, and entanglement

The Wehrl entropy is an associated to the Husimi quasi-probability distribution. We discuss how it can be used formulate entropic uncertainty relations and for a quantification of entanglement in continuous variables. show that Wehrl-Lieb inequality closer equality than usual Bia{\l}ynicki-Birula Mycielski relation almost everywhere. Furthermore, we mutual information obtain measurable perfect witness pure state bipartite entanglement, which additionally provides lower bound on entropy.