Majorization and the interconversion of bipartite states

Majorization is a powerful, easy-to-use and flexible tool which arises frequently in quantum mechanics as a consequence of fundamental connections between unitarity and the majorization relation. Entanglement theory does not escape from its influence. Thus the interconversion of bipartite pure states by means of local manipulations turns out to be ruled to a great extend by majorization relations. This review both introduces some elements of majorization theory and describes recent results on bipartite entanglement transformations, with special emphasis being placed on explaining the connections between these two topics. The latter implies analyzing two other aspects of quantum mechanics similarly influenced by majorization, namely the problem of mixing of quantum states and the characterization of quantum measurement.