  External environment influences on Grover's search algorithm modeled by
quantum noise are investigated. The algorithm is shown to be robust under that
external dissipation. Explicitly we prove that the resulting search positive
maps acting on unsorted N-dimensional database made of projective density
matrices depend on x the strength of the environment, and that there are
infinitely many x values for which search is successful after O(\sqrt{N})
queries. These algorithms are quantum entropy increasing.
