Improving the efficiency of single and multiple teleportation protocols based on the direct use of partially entangled states

•Optimal direct teleportation protocols using directly partially entangled states.•We put in a single formalism all strategies of direct teleportation.•We extend these techniques for multipartite partially entangle states.•We give upper bounds for the optimal efficiency of these protocols.

We push the limits of the direct use of partially pure entangled states to perform quantum teleportation by presenting several protocols in many different scenarios that achieve the optimal efficiency possible. We review and put in a single formalism the three major strategies known to date that allow one to use partially entangled states for direct quantum teleportation (no distillation strategies permitted) and compare their efficiencies in real world implementations. We show how one can improve the efficiency of many direct teleportation protocols by combining these techniques. We then develop new teleportation protocols employing multipartite partially entangled states. The three techniques are also used here in order to achieve the highest efficiency possible. Finally, we prove the upper bound for the optimal success rate for protocols based on partially entangled Bell states and show that some of the protocols here developed achieve such a bound.