Three-mode entanglement by interlinked nonlinear interactions in optical $\chi^{(2)}$ media

We address the generation of fully inseparable three-mode entangled states of radiation by interlinked nonlinear interactions in $\chi^{(2)}$ media. We show how three-mode entanglement can be used to realize symmetric and asymmetric telecloning machines, which achieve optimal fidelity for coherent states. An experimental implementation involving a single nonlinear crystal where the two interactions take place simultaneously is suggested. Preliminary experimental results showing the feasibility and the effectiveness of the interaction scheme with seeded crystal are also presented.