A family of generalized quantum entropies: definition and properties

G. M. Bosyk, S. Zozor, F. Holik, M. Portesi, P. W. Lamberti

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)3393-3420
Number of pages28
JournalQuantum Information Processing
Issue number8
Publication statusPublished - 1 Aug 2016


  • Entanglement detection
  • Majorization relation
  • Quantum entropies


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