  We introduce a tomography approach to describe the optical response of a
cavity quantum electrodynamics device, beyond the semiclassical image of
polarization rotation, by analyzing the polarization density matrix of the
reflected photons in the Poincar\'e sphere. Applying this approach to an
electrically-controlled quantum dot-cavity device, we show that a single
resonantly-excited quantum dot induces a large optical polarization rotation by
$20^\circ$ in latitude and longitude in the Poincar\'e sphere, with a
polarization purity remaining above $84\%$. The quantum dot resonance
fluorescence is shown to contribute to the polarization rotation via its
coherent part, whereas its incoherent part contributes to degrading the
polarization purity.
