Necessary and Sufficient Conditions of Separability for Multipartite Pure States∗

Abstract In this paper we present a necessary and sufficient condition of separability for multipartite pure states and variants of it. These conditions are very simple and calculable, and they do not require Schmidt decomposition (for two subsystems) or tracing out operations. We also give a necessary condition for a local unitary equivalence class for a bipartite system in terms of the determinant of the matrix of amplitudes. PACS numbers: 03.67.Lx, 03.67.Hk Key words: entanglement, quantum computing, separabilit