Dispersion and fidelity in quantum interferometry
David S. Simon, Alexander V. Sergienko, Thomas B. Bahder · Physical Review A · 2008
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, maximally path-entangled $\ensuremath{\mid}N,0⟩+⟨{0}_{,}N\ensuremath{\mid}$ (``N00N'') states, and photon pairs from parametric down-conversion. Assuming there is a phase shift ${\ensuremath{\phi}}_{0}$ in one arm of the interferometer, we compute the probabilities of measurement outcomes as a function of ${\ensuremath{\phi}}_{0}$, and then compute the Shannon mutual information between ${\ensuremath{\phi}}_{0}$ 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 down-conversion for which probabilities can be explicitly computed analytically, and which serves as a limiting case of the more realistic down-conversion model.