A family of generalized quantum entropies: definition and properties

We present a quantum version of the generalized ( h , ϕ ) -entropies, introduced by Salicrú et al. for the study of classical probability distributions. We establish their basic properties and show that already known quantum entropies such as von Neumann, and quantum versions of Rényi, Tsallis, and...

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Bibliographic Details
Published inQuantum information processing Vol. 15; no. 8; pp. 3393 - 3420
Main Authors Bosyk, G. M., Zozor, S., Holik, F., Portesi, M., Lamberti, P. W.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2016
Springer Verlag
Subjects
Data Structures and Information Theory
Information Theory
Mathematical Physics
Mathematics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Entanglement detection
Quantum entropies
Majorization relation
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Summary:We present a quantum version of the generalized ( h , ϕ ) -entropies, introduced by Salicrú et al. for the study of classical probability distributions. We establish their basic properties and show that already known quantum entropies such as von Neumann, and quantum versions of Rényi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicrú form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum ( h , ϕ ) -entropies under the action of quantum operations and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement and introduce a discussion on possible generalized conditional entropies as well.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-016-1329-5