Dicke states as matrix product states

We derive an exact canonical matrix product state (MPS) representation for Dicke states $\mathrm{\mid }{D}_k^n⟩$ with minimal bond dimension $\chi =k+1$, for general values of $n$ and $k$, for which the W-state is the simplest case $k=1$. We use this MPS to formulate a quantum circuit for sequentially preparing Dicke states deterministically, relating it to the recursive algorithm of Bärtschi and Eidenbenz. We also find exact canonical MPS representations with minimal bond dimension for higher-spin and qudit Dicke states.