  We construct generally applicable short-time perturbative expansions for some
fidelities, such as the input-output fidelity, the entanglement fidelity, and
the average fidelity. Successive terms of these expansions yield characteristic
times for the damping of the fidelities involving successive powers of the
Hamiltonian. The second-order results, which represent the damping rates of the
fidelities, are extensively discussed. As an interesting application of these
expansions, we use them to study the spatially-correlated dissipation of
quantum bits. Spatial correlations in the dissipation are described by a
correlation function. Explicit conditions are derived for independent
decoherence and for collective decoherence.
