We introduce a potential of multipartite entanglement for a system of n qubits, as the average over all balanced bipartitions of a bipartite entanglement measure, the purity. We study in detail its expression and look for its minimizers, the maximally multipartite entangled states. They have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. We investigate their structure and consider several examples for small n.
Cite this article
Paolo Facchi, Multipartite entanglement in qubit systems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 20 (2009), no. 1, pp. 25–67DOI 10.4171/RLM/532