Assisted Cloning of an Arbitrary Unknown d-Dimension State

Abstract

The purpose of this article is to further investigate the assisted cloning of a d-dimensional arbitrary unknown state by utilizing quantum teleportation (QT) and remote state preparation (RST) techniques. We first propose a scheme for cloning an arbitrary unknown single-qudit state with assistance from a state preparer. In this scheme, the maximally and non-maximally bipartite d-dimensional states are used as quantum channels, respectively. In the first stage of scheme requires usual QT and in the second stage, the state preparer disentangles the left over entangled states by introducing one auxiliary qudit and performing a generalized CNOT, a single-qudit positive operator-valued measurement (POVM) and a single-qudit projective measurement process and conveys some classical messages to different parties so that a copy is produced probabilistically with the unit fidelity. Then by replacing the maximally or non-maximally bipartite d-dimensional entangled channel with a sequence of maximally or non-maximally bipartite d-dimensional entangled states as a quantum channel, we can extend the above scheme to the case of cloning a d-dimensional arbitrary unknown m-qudit state with the unit fidelity and a certain probability in the help of the state preparer.