Multiparticle reduced density matrix and a useful kind of entangled state for quantum teleportation

It is pointed out that the possibility of teleporting an arbitrary unknown one-particle spin state is crucially connected with the maximal entanglement of the Einstein-Podolsky-Rosen pair, whose one-particle reduced density matrix is ρ(i)=(1/2)I2 (i=1,2). It is shown that, to teleport an arbitrary k-particle spin state, one must prepare an ancillary N-particle (N≥2k) entangled state, whose k-particle reduced density matrix has the form (1/2k)I2k (I2k is the 2kx2k identity matrix). An alternative approach to constructing many-particle entangled states is developed by using Rx(π), the collective rotation of π around a given axis (say, x axis). The entangled states constructed by using Rx(π) operating on the basis of angular momentum uncoupling representation are just the GHZ states, which cannot be used for the teleportation of an arbitrary k (≥2) particle spin state. The entangled states constructed by using Rx(π) operating on the basis of angular momentum coupling representation turn out to be effective for the teleportation of an arbitrary multiparticle state. A formal extension of the scheme of Bennett et al. to deal with the teleportation of an arbitrary two (or more) particle spin state is discussed