  There has been an extensive development in the use of multi-partite
entanglement as a resource for various quantum information processing tasks. In
this paper we focus on preparing arbitrary spin eigenstates whose subset
contain important entangled resources like Dicke states as well as some other
sub-radiant states that are difficult to prepare. Leveraging on the symmetry of
these states we consider uniform pairwise exchange coupling between every pair
of qubits. Starting from a product state of a given spin eigenstate with a
single qubit state, another spin eigenstate can be prepared using simple time
evolutions. This expansion paves a deterministic approach to prepare arbitrary
Dicke states in linear steps. We discuss an improvement in this cost building
up on a previous work for W states deterministic preparation in logarithmic
circuit depth. The modified algorithm requires several iterations of pumping
spin angular momentum into the system and is akin to the amplitude
amplification in Grover search. As a use case to demonstrate the proposed
scheme, we choose a system of non-interacting static spin qubits connected to a
ferromagnetic reservoir. The flying qubits emerging from the reservoir locally
interact with static qubits successively, mediating an in-direct exchange
interaction between all the pairs.
