Highly asymmetric quantum cloning in arbitrary dimension

We investigate the universal asymmetric cloning of states in a Hilbert space of arbitrary dimension. We derive the class of optimal and fully asymmetric 1→ 3 cloners, which produce three copies, each having a different fidelity. A simple parametric expression for the maximum achievable cloning fidelity triplets is then provided. As a side-product, we also prove the optimality of the 1 → 2 asymmetric cloning machines that have been proposed in the literature.