Optimal asymmetric 1 → 4 quantum cloning in arbitrary dimension

We present an optimal asymmetric 1 → 4 quantum cloner. Our derivation generalizes the constructions of optimal asymmetric 1 → 2 and 1 → 3 quantum cloners in [Quantum Inf. Comput 5, 583 (2005)]. We explicitly prove the optimality of this cloner and give the maximum achievable fidelities. We also present the relation between the optimal quantum cloner with the multipartite entangled state which shows the singlet monogamy inequality in [Phys. Rev. Lett. 103, 050501 (2009)]