Entanglement teleportation through GHZ-class states

We first consider teleportation of entangled states shared between Claire and Alice to Bob1 and Bob2 when Alice and the two Bobs share a single copy of a GHZ state and where all the four parties are at distant locations. We extend this result to a more general state than GHZ-state and show that still a class of pure entangled states can be teleported, where the entanglement of this class ranges from 0 to e (≤1), depending on the entanglement (defined in the text) of the channel state. We then generalize this situation to the case of teleportation of entangled states shared between Claire1,Claire2, . . . ,Claire(N − 1) and Alice to Bob1,Bob2, . . . ,BobN when Alice and the N Bobs share a single copy of a GHZ-class state and where again all the 2N parties are at distant locations. Quantum teleportation, proposed by Bennett Brassard, Crepeau, Jozsa, Peres and Wootters (BBCJPW) [1], is a protocol by which the information of an arbitrary state of a quantum mechanical system can be transferred (teleported) exactly from one location (where say, Alice is operating) to a possibly distant location (operated say, by Bob) by using only local operations and classical communication, without sending the system itself (thus, at Bob’s location, the exact † Present address: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland. New Journal of Physics 4 (2002) 48.1–48.9 PII: S1367-2630(02)35846-4 1367-2630/02/000048+9$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft