  We address the case, when querying to the oracle in Grover's algorithm is
exposed to noise including phase distortions. The oracle-box wires can be
altered by an opposite party that tries to prevent correct receiving data from
the oracle. This situation reflects an experienced truth that any access to
prophetic knowledge cannot be common and direct. To study the problem, we
introduce a simple model of collective phase distortions on the base of phase
damping channel. In the model used, the success probability is not altered via
the oracle-box wires {\it per se}. Phase distortions of the considered type can
hardly be detected via any one-time query to the oracle. However, the success
probability is significantly changed, when such errors are introduced as an
intermediate step into the Grover iteration. We investigate the success
probability with respect to variations the parameter that characterizes the
amount of phase errors. It turns out that the success probability is decreased
significantly even if the error amount is not very high. Moreover, this
probability quickly reduces to the value of one half, which corresponds to the
completely mixed state. We also study trade-off relations between quantum
coherence and the success probability in the presence of noise of the
considered type.
