MiS Preprint Repository

Faithful teleportation of an unknown state $|\phi\rangle$ in ${\mathbb{C}}^d$ is considered, where a general entangled state $\rho$ is served as the resource. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation channel $\rho$ in ${\mathbb{C}}^m \otimes {\mathbb{C}}^d $ and ${\mathbb{C}}^d \otimes {\mathbb{C}}^n $ are derived. It is shown that for $\rho$ in ${\mathbb{C}}^m \otimes {\mathbb{C}}^d $, $\rho$ must be a maximally entangled state, while for $\rho$ in $ {\mathbb{C}}^d \otimes{\mathbb{C}}^n $, $\rho$ must be a mixed or pure maximally entangled state. Furthermore, the sender's measurements must be all projectors of maximally entangled states. On the other hand, for $m,\,n > d$, we present some classes of states for faithful teleportation.