Generalized disorder measures and the detection of quantum entanglement

We discuss the main properties of general non-additive entropic forms based on arbitrary concave functions and their relation with the theory of majorization. As application, we examine the generalized entropic criterion for separability of mixed states of composite quantum systems, where non-additive disorder measures play a fundamental role. These features are then analyzed in two-qubit and two-qudit systems, where it is seen that the von Neumann-based criterion is especially weak for detecting entanglement, in contrast with those based on the Tsallis and other non-additive disorder measures.