  We derive a tight upper bound for the fidelity of a universal N to M qubit
cloner, valid for any M \geq N, where the output of the cloner is required to
be supported on the symmetric subspace. Our proof is based on the concatenation
of two cloners and the connection between quantum cloning and quantum state
estimation. We generalise the operation of a quantum cloner to mixed and/or
entangled input qubits described by a density matrix supported on the symmetric
subspace of the constituent qubits. We also extend the validity of optimal
state estimation methods to inputs of this kind.
