Generalised asymmetric quantum cloning machines

We study machines that take N identical replicas of a pure qudit state as input and output a set of MA clones of a given fidelity and another set of MB clones of another fidelity. The trade-off between these two fidelities is investigated, and numerous examples of optimal N → MA + MB cloning machines are exhibited using a generic method. A generalisation to more than two sets of clones is also discussed. Finally, an optical implementation of some such machines is proposed. This paper is an extended version of [Phys. Rev. A 72, 042328 (2005)].