Collective processes of an ensemble of spin-1/2 particles

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.