Analysis of practical phase sensing with Quantum Interferometers

In phase sensing with quantum interferometers, likelihood estimation is used to obtain the estimated value of the measured phase. Moreover, the precision for such sensors depends on the total phase difference between the two paths of the interferometer. To determine the optimal operation parameters of the interferometer, fisher information analysis is required. Both objectives, i.e. likelihood estimation and performance optimization, require knowledge of the probabilities for different events as a function of the phase difference τ. In this article we drive expressions for these probabilities considering the effects of practical parameters like the interferometer’s visibility, the optical pulse width, and the effect of imperfect detectors. Furthermore, we depict fisher information curves for some chosen input states showing the effects of reduced visibility and short pulse widths.