Collective States and Symmetric Local Decoherence in Large Ensembles of Qubits

The symmetric collective states of an atomic spin ensemble (i.e., many-body states that are invariant under particle exchange) are not preserved by decoherence that acts identically but individually on members of the ensemble. We develop a class of collective states in an ensemble of N spin-1/2 particles that is invariant under symmetric local decoherence and find that the dimension of the Hilbert space spanned by these collective states scales only as N^2. We then investigate the open system dynamics of experimentally relevant non-classical collective atomic states, including Schroedinger cat and spin squeezed states, subject to various symmetric but local decoherence models.