Three qubits can be entangled in two inequivalent ways - art. no. 062314

Invertible local transformations of a multipartite system are used to defin e equivalence classes in the set of entangled states. This classification c oncerns the entanglement properties of a single copy of the state. Accordin gly, we say that two states have the same kind of entanglement if both of t hem can be obtained from the other by means of local operations and classic al communication (LOCC) with nonzero probability. When applied to pure stat es of a three-qubit system, this approach reveals the existence of two ineq uivalent kinds of genuine tripartite entanglement, for which the Greenberge r-Horne-Zeilinger state and a W state appear as remarkable representatives. In particular, we show that the Wstate retains maximally bipartite entangl ement when any one of the three qubits is traced out. We generalize our res ults both to the case of higher-dimensional subsystems and also to more tha n three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, no t even with a small probability of success.