Tripartite loss model for Mach-Zehnder interferometers with application   to phase sensitivity : Complete expressions for measurement operator mean   values, variances, and cross correlations
  A generalized analytical tripartite loss model is posited for Mach-Zehnder interferometer (MZI) phase sensitivity which is valid for both arbitrary photon input states and arbitrary system environmental states. This model is shown to subsume the phase sensitivity models for the lossless MZI and the ground state MZI. It can be employed to develop specialized models useful for estimating phase sensitivities, as well as for performing associated design trade-off analyses, for MZIs which operate in environmental regimes that are not contained within the ground state MZI's envelope of validity. As a simple illustration of its utility, the model is used to develop phase sensitivity expessions for an MZI with "excited" internal arms and an MZI with "excited" output channels. These expressions yield a conditional relationship between the expected number of photons entering an MZI and its efficiency parameters which-when satisfied-predicts an enhanced phase sensitivity for the MZI with "excited" output channels relative to that for the MZI with "excited" internal arms. 
A. D. Parks, S. E. Spence, J. E. Troupe