Quantum key distribution by teleportation and unextendible product operator bases

Abstract

Quantum teleportation and quantum key distribution (QKD) both play a key role in the application of quantum information processing. They have been widely realized in experiments in the past decades. We construct a multipartite QKD protocol using teleportation by a Greenberger-Horne-Zeilinger entangled state. The latter is a frequently studied family entangled states in theory and experiments. Our protocol shows the security because the loss of any particles does not lead to the loss of information the sender wants to send to the receiver. Further, the classical messages cost in the protocol occur only among some particles. We also apply the unextendible product operator basis (UPOB) by performing them on high dimensional states, which are then teleported to the receiver. We stress that UPOBs are related to quantum nonlocality, which is associated with the local indistinguishability of orthogonal states. Hence our paper may contribute to the novel understanding of quantum nonlocality, as well as related quantum-information tasks such as state and operation discrimination.