  When a harmonic oscillator is under the influence of a Gaussian process such
as linear damping, parametric gain, and linear coupling to a thermal
environment, its coherent states are transformed into states with Gaussian
Wigner function. Qubit states can be encoded in the |0> and |1> Fock states of
a quantum harmonic oscillator, and it is relevant to know the fidelity of the
output qubit state after a Gaussian process on the oscillator. In this paper we
present a general expression for the average qubit fidelity in terms of the
first and second moments of the output from input coherent states subjected to
Gaussian processes.
