  We present a semiconductor master equation technique to study the
input/output characteristics of coherent photon transport in a semiconductor
waveguide-cavity system containing a single quantum dot. We use this approach
to investigate the effects of photon propagation and anharmonic cavity-QED for
various dot-cavity interaction strengths, including weakly-coupled,
intermediately-coupled, and strongly-coupled regimes. We demonstrate that for
mean photon numbers much less than 0.1, the commonly adopted weak excitation
(single quantum) approximation breaks down, even in the weak coupling regime.
As a measure of the anharmonic multiphoton-correlations, we compute the Fano
factor and the correlation error associated with making a semiclassical
approximation. We also explore the role of electron--acoustic-phonon scattering
and find that phonon-mediated scattering plays a qualitatively important role
on the light propagation characteristics. As an application of the theory, we
simulate a conditional phase gate at a phonon bath temperature of $20 $K in the
strong coupling regime.
