  We show that injecting a light pulse prepared in the Shroedinger cat quantum
state into the dark port of a two-arm interferometer and the strong classical
light into the bright one, it is possible, in principle, to detect a given
phase shift unambiguously. The value of this phase shift is inversely
proportional to the amplitudes of both the classical carrier and Shroedinger
cat state. However, an exotic detection procedure is required for this purpose.
By measuring the number of photons at the output dark port, it is possible to
detect the phase shift with the vanishing "false positive" probability. The
"false negative" probability in this case decreases with the increase on the
amplitude of the Schroedinger cat state and, for reasonable values of this
amplitude, can be made as small as about 0.1.
