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Faithful teleportation with arbitrary pure or mixed resource states

We study faithful teleportation systematically with arbitrary entangled states as resources. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation of an unknown state |ϕ> in C^d with an entangled resource ρ in C^m \otimes C^d and C^d \otimes C^n are derived. It is shown that for ρ in C^m\otimesC^d, ρ must be a maximally entangled state, while for ρ in C^d \otimes C^n, ρ must be a puremaximally entangled state. Moreover, we show that the sender's measurements must be all projectors of maximally entangled pure states. The relations between the entanglement of the formation of the resource states and faithful teleportation are also discussed.