Possibility of quantum teleportation and the reduced density matrix

It is shown that only the maximally entangled two-particle (spin 1/2) state s whose one-particle reduced density matrix is rho (i) = (1/2)I-2 can reali ze the teleportation of an arbitrary one-particle spin state. Based on this , to teleport an arbitrary k-particle spin state, one must prepare an N-par ticle entangled state whose Ic-particle (k < N) reduced density matrix has the structure 2(-k)I(2k) (I-2k being the 2(k) x 2(k) identity matrix). The N-particle Greenberger-Horne-Zeilinger states cannot realize the teleportat ion of an arbitrary k-particle (N > k greater than or equal to 2) state, ex cept for special states with only two components.