A family of generalized quantum entropies: definition and properties

Abstract

We present a quantum version of the generalized $(h,\varphi )$-entropies, introduced by Salicrú \textit{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 $(h,\varphi )$-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.

26 pages, 1 figure. Close to published version

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• Generalized non-additive entropies and quantum entanglement
• Some general properties of unified entropies
• Subadditivity of q-entropies for q>1
• Rényi entropy uncertainty relation for successive projective measurements
• Violation of majorization relations in entangled states and its detection by means of generalized entropic forms
• Rényi generalizations of quantum information measures
• Unified entropic measures of quantum correlations induced by local measurements

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