  Two novel schemes are proposed for the dissipative preparation of large W
states, of the order of ten qubits, within the context of Cavity QED. By
utilizing properties of the irreducible representations of su(3), we are able
to construct protocols in which it is possible to restrict the open system
dynamics to a fully symmetric irreducible subspace of the total Hilbert space,
and hence obtain analytic solutions for effective ground state dynamics of
arbitrary sized ensembles of $\Lambda$ atoms within an optical cavity. In the
proposed schemes, the natural decay processes of spontaneous emission and
photon loss are no longer undesirable, but essential to the required dynamics.
All aspects of the proposed schemes relevant to implementation in currently
available optical cavities are explored, especially with respect to increasing
system size.
