  We determine the minimal number of qubits that it is necessary to have access
to in order to transform Dicke states into other Dicke states. In general, the
number of qubits in Dicke states cannot be increased via transformation gates
by accessing only a single qubit, in direct contrast to other multipartite
entangled states such as GHZ, W and cluster states. We construct a universal
optimal gate which adds spin-up qubits or spin-down qubits to any Dicke state
by minimal access. We also show the existence of a universal gate which
transforms any size of Dicke state as long as it has access to at least the
required number of qubits. Our results have important consequences for the
generation of Dicke states in physical systems such as ion traps, all-optical
setups and cavity-QED settings where they can be used for a variety of quantum
information processing tasks.
