Bidirectional Assisted Cloning for Arbitrary Unknown Single-Qubit States

In this article, we first present a new scheme that can simultaneously produce two perfect replicas of arbitrary unknown single-qubit states in two different directions with the aid provided by a state preparer. This scheme can be divided into two stages: bidirectional quantum teleportation (BQT) and assisted cloning (AC). The first stage of this scheme requires a BQT through a maximally entangled four-qubit cluster state as the quantum channel, where the arbitrary unknown single-qubit states of two communicators are simultaneously exchanged and in the second stage, the state preparer uses a special two-qubit projective measurement (PM) to disentangle the remaining entangled states and informs different participants of some classical information so as to generate perfect replicas or orthogonal complement replicas. The research results indicate that this scheme can generate a perfect replica or orthogonal complement replica of an arbitrary unknown single-qubit state at each of two distant locations simultaneously, with the help of the state preparer. Subsequently, by replacing the quantum channel in the above scheme with a non-maximally entangled four-qubit cluster state, the above scheme is generalized from the aspects of PM and positive operator-value measurement (POVM), respectively after introducing an appropriate number of auxiliary qubits.