“…Finally, we address the degrading effects owing to the experimental imperfections, extending our treatment to include these in the analysis of the FI. In most interesting cases, the photon-loss process, determined by a given strength η loss , and the nonunit efficiency detection, designated by η eff , can be regarded as the major limits to interferometric precision [21,22,25,26,28,38,55,56,[81][82][83][84]. Furthermore, it is customary to assume that the environmental noise and photonloss mechanism act identically and independently upon each probe mode [85], and that the environment is in a thermal state at a temperature determined by the mean photon number n th .…”