Phase estimation with nonunitary interferometers: Information as a metric

Determining the phase in one arm of a quantum interferometer is discussed taking into account the three nonideal aspects in real experiments: nondeterministic state preparation, nonunitary 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 nonideal 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 nonideal 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.