A family of generalized quantum entropies: definition and properties

GM Bosyk, S Zozor, F Holik, M Portesi… - Quantum Information …, 2016 - Springer
Quantum Information Processing, 2016Springer
We present a quantum version of the generalized (h, ϕ)(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 …
Abstract
We present a quantum version of the generalized -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 -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.
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