  When a photon interferes with itself while traversing a Mach-Zehnder
inteferometer, the output port where it emerges is influenced by the phase
difference between the interferometer arms. This allows for highly precise
estimation of the path length difference (delay) but is extremely sensitive to
phase noise. By contrast, a delay between the arms of the two-photon
Hong-Ou-Mandel interferometer directly affects the relative
indistinguishability of the photon pair, affecting the rate of recorded
coincidences. This likewise allows for delay estimation; notably less precise
but with the advantage of being less sensitive to perturbations of the photons'
phase. Focusing on two-photon input states, we here investigate to what degree
of noise Mach-Zehnder interferometry retains its edge over Hong-Ou-Mandel
interferometry. We also explore the competing benefits of different two-photon
inputs for a Mach-Zehnder interferometer, and under what parameter regimes each
input performs best.
