Wehrl entropy, entropic uncertainty relations and entanglement

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 Białynicki-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.

arXiv comment15 pages, 3 figures

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• General class of continuous variable entanglement criteria
• Detecting continuous variable entanglement in phase space with the $Q$-distribution
• Quantum and classical contributions to entropy production in fermionic and bosonic Gaussian systems
• Relative entropic uncertainty relation for scalar quantum fields
• Accessing continuous-variable entanglement witnesses with multimode spin observables
• Entropic distinguishability of quantum fields in phase space
• Relating the Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions operationally through the quantum limited amplifier and attenuator channels
• A tomographic approach to the sum uncertainty relation and quantum entanglement in continuous variable systems
• Area laws and thermalization from classical entropies in a Bose-Einstein condensate
• Entropy estimation in a spin-1 Bose-Einstein condensate
• Interferometric detection of continuous-variable entanglement using two states
• Relative Entropy and Mutual Information in Gaussian Statistical Field Theory
• Phase space distributions in information theory
• A numerical study of the Bose-Einstein condensates in a double-well trap using finite differences
• Detecting strongly non-Gaussian entanglement
• Information and majorization theory for fermionic phase-space distributions