Optimal ancilla-free phase-covariant telecloning of qudits via nonmaximally entangled states

We study the one-to-two phase-covariant telecloning of a qudit without ancilla. We show that the fidelity of the two clones can reach that of the clones in the optimal ancilla-based one-to-two phase-covariant cloning and telecloning, i.e., the limitation of quantum mechanics. More interestingly, it is a nonmaximally entangled state rather than the maximally entangled state that can be used to realize such a telecloning task.