Violation of majorization relations in entangled states and its detection by means of generalized entropic forms

We examine the violation of the majorization relations between the eigenvalues of the full and reduced density operators of entangled states of composite systems and its detection using generalized entropic forms based on arbitrary concave functions. It is shown that the violation of these relations may not always be detected by the conditional von Neumann and Tsallis entropies (for any $q>0$). Families of smooth entropic forms which are always able to detect such violations are, however, provided. These features are then examined for particular sets of mixed states in a two-qudit system, which for $d\geq 3$ may exhibit different types of violation of the majorization relations. Comparison with the Peres criterion for separability is also shown.