  Determining the phase in one arm of a quantum interferometer is discussed
taking into account the three non-ideal aspects in real experiments:
non-deterministic state preparation, non-unitary state evolution due to losses
during state propagation, and imperfect state detection. A general expression
is written for the probability of a measurement outcome taking into account
these three non-ideal aspects. As an example of applying the formalism, the
classical Fisher information and fidelity (Shannon mutual information between
phase and measurements) are computed for few-photon Fock and N00N states input
into a lossy Mach-Zehnder interferometer. These three non-ideal aspects lead to
qualitative differences in phase estimation, such as a decrease in fidelity and
Fisher information that depends on the true value of the phase.
