  When the dynamics of a spin ensemble are expressible solely in terms of
symmetric processes and collective spin operators, the symmetric collective
states of the ensemble are preserved. These many-body states, which are
invariant under particle relabeling, can be efficiently simulated since they
span a subspace whose dimension is linear in the number of spins. However, many
open system dynamics break this symmetry, most notably when ensemble members
undergo identical, but local, decoherence. In this paper, we extend the
definition of symmetric collective states of an ensemble of spin-1/2 particles
in order to efficiently describe these more general collective processes. The
corresponding collective states span a subspace which grows quadratically with
the number of spins. We also derive explicit formulae for expressing arbitrary
identical, local decoherence in terms of these states.
