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

We show that injecting a light pulse prepared in the Shrodinger cat quantum state into the dark port of a two-arm interferometer, it is possible to detect a given phase shift unambiguously. The value of this phase shift is inversely proportional to the amplitudes of both the classical carrier light and the Shrodinger cat state. However, an unconventional 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 a vanishing 'false positive' probability. The 'false negative' probability in this case decreases as the amplitude of the Schrodinger cat state increases and, for reasonable values of this amplitude, can be made less than about 0.1.