  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.
