Faithful teleportation with partially entangled states

Abstract

We write explicitly a general protocol for faithful teleportation of a $d$-state particle (qudit) via a partially entangled pair of (pure) $n$-state particles. The classical communication cost (CCC) of the protocol is ${\mathrm{log}}_{2}(nd)$ bits, and it is implemented by a projective measurement performed by Alice, and a unitary operator performed by Bob (after receiving from Alice the measurement result). We prove the optimality of our protocol by a comparison with the concentrate and teleport strategy. We also show that if $d>n∕2$, or if there is no residual entanglement left after the faithful teleportation, the CCC of any protocol is at least ${\mathrm{log}}_{2}(nd)$ bits. Furthermore, we find a lower bound on the CCC in the process transforming one bipartite state to another by means of local operation and classical communication.