Wehrl entropy is an entropy associated with the Husimi quasiprobability distribution. We discuss how it can be used to formulate entropic uncertainty relations and for a quantification of entanglement in continuous variables. We show that the Wehrl-Lieb inequality is closer to equality than the usual Białynicki-Birula–Mycielski entropic uncertainty relation almost everywhere. Furthermore, we show how Wehrl mutual information can be used to obtain a measurable perfect witness for pure state bipartite entanglement, which additionally provides a lower bound on the entanglement entropy.
S. Floerchinger, T. Haas, H. Müller-Groeling, “Wehrl entropy, entropic uncertainty relations, and entanglement”, Phys. Rev. A 103, 062222 (2021).
Related to Project A06