We construct generally applicable short-time perturbative expansions for somefidelities, such as the input-output fidelity, the entanglement fidelity, andthe average fidelity. Successive terms of these expansions yield characteristictimes for the damping of the fidelities involving successive powers of theHamiltonian. The second-order results, which represent the damping rates of thefidelities, are extensively discussed. As an interesting application of theseexpansions, we use them to study the spatially-correlated dissipation ofquantum bits. Spatial correlations in the dissipation are described by acorrelation function. Explicit conditions are derived for independentdecoherence and for collective decoherence.
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