Federico Holik

A family of generalized quantum entropies: definition and properties

We present a quantum version of the generalized

A quantum logical and geometrical approach to the study of improper mixtures

(h,\phi )

Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory

(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

Quantal effects and MaxEnt

(h,\phi )

Geometric probability theory and Jaynes’s methodology

(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.

Generalized entropies in quantum and classical statistical theories

Let