Wehrl entropy, entropic uncertainty relations and entanglement

• URL: http://arxiv.org/abs/2103.07229v2
• Date: Mon, 28 Jun 2021 17:52:30 GMT
• Title: Wehrl entropy, entropic uncertainty relations and entanglement
• Authors: Stefan Floerchinger, Tobias Haas, Henrik M\"uller-Groeling
• Abstract summary: We show that the Wehrl-Lieb inequality is closer to equality than the usual Bialynicki-Birula and Mycielski entropic uncertainty relation almost everywhere. We show how a Wehrl mutual information can be used to obtain a measurable perfect witness for pure state bipartite entanglement.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Wehrl entropy is an entropy associated to the Husimi quasi-probability 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 Bia{\l}ynicki-Birula and Mycielski entropic uncertainty relation almost everywhere. Furthermore, we show how a 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.

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