Using Schroedinger cat quantum state for detection of a given phase shift

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.