Asymmetric Bidirectional 3 ⇔ 2 Qubit Teleportation Protocol Between Alice and Bob Via 9-qubit Cluster State

In this paper we present a protocol to perform the task of a bilateral exchange of entanglements between two parties in the case where one of the parties holds a three particle entangled state where the other party holds a two particle entangled state. The protocol is supervised by a controller. The quantum channel used here is a nine particle entangled state. The speciality of the protocol is that in all the involved measurements only a fraction of the possible measurement outcomes appear which substantially simplifies the protocol. Our scheme is a perfect teleportation scheme, that is, the mutual transfer of entangled states is performed with certainty.