Hybrid economical telecloning of equatorial qubits and generation of multipartite entanglement

We propose a simple scheme for hybrid economical telecloning (HETC) of equatorial qubits with the well-known W-type entangled states. The so-called HETC is a synthesis of several types of quantum cloning and quantum teleportation, in which economical symmetric and asymmetric clonings and anticlonings can be simultaneously achieved by teleportation. We use the global fidelity and average-single-qubit fidelity to estimate, respectively, the collective copying quality and show that the two criteria lead to different results. We obtain interesting equalities and inequalities about the fidelities of clones or anticlones. We also introduce controlled HETC of equatorial qubits with recently proposed Greenberger-Horne-Zeilinger (GHZ)-W-type entangled states [L. Chen and Y. X. Chen, Phys. Rev. A 74, 062310 (2006)], in which the achievement of phase-covariant telecloning between the sender (Alice) and the receivers (Bobs) is conditioned on the collaboration of all the supervisors (Charlies). This idea may open a perspective for the applications of such interesting type of entangled states. A method for generating the GHZ-W-type entangled states is also presented.