Generalized entropies and quantum entanglement

We discuss the fundamental properties of general entropic forms based on arbitrary concave functions and their application to current problems of quantum information theory. It is first shown that the extended formalism allows to construct, for a two-qubit system, least biased density operators which possess minimum entanglement for any data based on Bell constraints, avoiding fake entanglement. We next discuss the generalized entropic criterion for separability of mixed states of bipartite quantum systems, and its relation with the disorder criterion.