Possibility of Quantum Teleportation and the Reduced Density Matrix

It is shown that only the maximally entangled two-particle (spin 1/2) states whose one-particle reduced density matrix is ρ(i) = (1/2)I₂ can realize 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-particle entangled state whose k-particle (k < N) reduced density matrix has the structure 2^-kI_2^k (I_2^k being the 2^k x 2^k identity matrix). The N-particle Greenberger-Horne-Zeilinger states cannot realize the teleportation of an arbitrary k-particle (N > k ≥ 2) state, except for special states with only two components.