Schmidt measure as a tool for quantifying multiparticle entanglement

We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multipartite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on the full state space, and is shown to be an entanglement monotone, that is, it cannot increase under local quantum operations with classical communication and under mixing. For a large class of mixed states this measure of entanglement can be calculated exactly, and it provides a detailed classification of mixed states.