  The concept of fidelity has been introduced to characterize the stability of
a quantum-mechanical system against perturbations. The fidelity amplitude is
defined as the overlap integral of a wave packet with itself after the
development forth and back under the influence of two slightly different
Hamiltonians. It was shown by Prosen and Znidaric in the linear-response
approximation that the decay of the fidelity is frozen if the Hamiltonian of
the perturbation contains off-diagonal elements only. In the present work the
results of Prosen and Znidaric are extended by a supersymmetry calculation to
arbitrary strengths of the perturbation for the case of an unperturbed
Hamiltonian taken from the Gaussian orthogonal ensemble and a purely unitary
antisymmetric perturbation. It is found that for the exact calculation the
freeze of fidelity is only slightly reduced as compared to the linear-response
approximation. This may have important consequences for the design of quantum
computers.
