Dispersion and fidelity in quantum interferometry

We consider Mach-Zehnder and Hong-Ou-Mandel interferometers with nonclassical states of light as input, and study the effect that dispersion inside the interferometer has on the sensitivity of phase measurements. We study in detail a number of different one- and two-photon input states, including Fock, dual Fock, N00N states, and photon pairs from parametric downconversion. Assuming there is a phase shift $\phi_0$ in one arm of the interferometer, we compute the probabilities of measurement outcomes as a function of $\phi_0$, and then compute the Shannon mutual information between $\phi_0$ and the measurements. This provides a means of quantitatively comparing the utility of various input states for determining the phase in the presence of dispersion. In addition, we consider a simplified model of parametric downconversion for which probabilities can be explicitly computed analytically, and which serves as a limiting case of the more realistic downconversion model.