Unidirectional and Bidirectional Controlled Assisted Cloning of an Arbitrary m-qudit State

Utilizing the ingeniously selected quantum channel, we first propose a universal protocol to deterministically achieve the assisted clone of an arbitrary m-qudit state. In the first stage of the protocol, controlled teleportation is carrying out to transmit the unknown state from the sender to the receiver under the supervision of a controller. In the second stage, with the aid of the preparer through suitable positive-operator-value measurement and projection measurement, the perfect copy of the initial state can be created at the sender’s location. Then we consider the two-way scenario and design another assisted-clone protocol. Comparing with the previous unidirectional and bidirectional assisted-clone protocols for multi-particle and high-dimensional states, which produce the unknown state and its orthogonal complement state, the proposed protocols create the perfect copy of the unknown state. Furthermore, we discuss the case that the quantum channel is non-maximally entangled.