An economical state-dependent telecloning for a multiparticle GHZ state

The scheme for a 1–3 economical state-dependent telecloning of a multiparticle GHZ state is proposed. It shows that every one of spatially separated three receivers obtains one copy which is dependent on original state. Fidelity can hit to the optimal fidelity 5/6. Meantime, we also propose a 1–3 asymmetric economical telecloning of a particular multiparticle GHZ state by parameterizing coefficients of state in the channel. The three fidelities can reach the best match that is the same as the symmetric case. Furthermore, the above two schemes can be generalized into the case of $1-M(M=2k+1,k>0)$ telecloning of a multiparticle GHZ state. Satisfying some certain conditions, optimal fidelities with $\frac{1}{2}+\frac{(M+1)}{4M}$ can be obtained. As without ancilla in the channel, the number of entangled particles is less than one in current schemes and fidelities can be optimal if the original state is an equatorial state.