Measurement of amplitude probability distributions for photon-number-operator eigenstates

A homodyne detector measures a field-amplitude component of the incoming signal. If the incoming signal is in an $n$-photon eigenstate the homodyne detector's output probability distribution exhibits $n$ fringes. Here the degree to which the visibility of these fringes is degraded by a homodyne detector with less than unit quantum efficiency is evaluated. An experiment employing conjugate pairs of photons generated via a parametric down conversion or four-wave mixing is proposed by which these fringes could be observed.