All Entanglements in a Multipartite System

We formalize concepts such as generalized party and generalized local operation, and consider all possible entanglements possessed by a multipartite state. It is pointed out that local operations and classical communication (LOCC) is a fixed point under any partition. As consequences of the principle that the entanglement among all the parties is not increased by LOCC as defined for all these parties, some general conclusions are obtained. Then generalizations of entanglement measures, applicable for each entanglement in a multipartite state, are proposed. Of all the entanglements in a N -partite system, the true N -partite entanglement is the one among all the N parties. Based on the conservation of each entanglement under reversible LOCC, a sufficient condition is obtained for any set of states not to be a reversible LOCC entanglement generating set (RLEGS). This leads to the conclusion that for more than two parties, the set of all GHZ-like states is not a RLEGS. PACS numbers: 03.65.Ud, 03.67.-a Typeset using REVTEX