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Generalized quantum entropies: a definition and some properties

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In this presentation, a family of quantum entropies inspired by the clasical (h,φ)- entropies proposed by Salicrú et al. (more precisely, inspired by the Csiszár’s divergen- cies) will be introduced. The proposed family includes several well-known entropies such that the von Neumann entropy or quantum versions of the Rényi’s and Havrda- Charvát-Daróczy-Tsallis’s entropies, among many others. The main properties of the proposed quantum (h, φ )-entropies lie on the the fundamental concept of majorization. The behavior of these entropies when a quantum state is subject to some quantum op- erations (unitary, measurement) will be characterized, and its behavior when dealing with composite systems as well. Some potential applications in detection of entan- glement will be exposed. Finally, we will present possible definitions of associate measures such that conditional generalized quantum entropies.
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hal-01422466 , version 1 (26-12-2016)


  • HAL Id : hal-01422466 , version 1


Steeve Zozor, Gustavo Martin Bosyk, Federico Holik, Mariela Portesi, P. W. Lamberti. Generalized quantum entropies: a definition and some properties. AMQI 2016 - International Workshop on Applied Mathematics & Quantum Information, Nov 2016, Cagliari, Italy. ⟨hal-01422466⟩
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