A characterization of multipartite entanglement

Entanglement is one of the most intriguing features of quantummechanics. Although it is widely used in quantum communication andinformation processing and plays a key role in quantum computation,it is not fully understood. It is deeply rooted into the linearityof quantum theory and in the superposition principle and basicallyconsists (for pure states) in the impossibility of factorizing thestate of the total system in terms of the states of its constituents.The quantification of entanglement is an open and challenging problem.It is possible to give a good definition of bipartite entanglement interms of the von Neumann entropy and the entanglement of formation. Theproblem of defining multipartite entanglement is more difficult and nounique definition exists.A method is proposed to characterize and quantify multipartiteentanglement for pure states. The method hinges upon the study of theprobability density function of bipartite entanglement and is tested onan ensemble of qubits in a variety of situations.The entanglement features of a class of random states is also analyzed.These states turn out to be very entangled and their entanglement ismultipartite, in a sense that can be precisely defined. We analiticallydetermine the thermodynamical limit of the purity of such states.