Possibility of Quantum Teleportation and the Reduced Density Matrix

Abstract

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 arbitraryone-particle spin state. Based on this, to teleport an arbitrary k-particlespin state, one must prepare an N-particle entangled state whosek-particle (k<N) reduced density matrix has the structure2-kI2k (I2k being the 2k×2k identity matrix).The N-particle Greenberger-Horne-Zeilinger states cannot realizethe teleportation of an arbitrary k-particle(N>k⩾2) state, except for special states with only two components.