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 ${\log }_2(nd)$ bits, and it is implemented by a {\em 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 {\em any} protocol is at least ${\log }_2(nd)$ 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 (LOCC).

arXiv comment5 pages, RevTex4, This significantly modified version accepted for publication in Phys. Rev. A

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