  In the framework of optical quantum computing and communications, a major
objective consists in building receiving nodes that implement conditional
operations on incoming photons, using the interaction with a single stationary
qubit. In particular, the quest for scalable nodes motivated the development of
cavity-enhanced spin-photon interfaces with solid-state emitters. An important
challenge remains, however, to produce a stable, controllable, spin-dependant
photon state, in a deterministic way. Here we use a pillar-based high-Q cavity,
embedding a singly-charged semiconductor quantum dot, to demonstrate the
control of giant polarisation rotations induced by a single electron spin. A
complete tomography approach is used to deduce the output polarisation Stokes
vector, conditioned by a single spin state. We experimentally demonstrate
rotation amplitudes such as $\pm \frac{\pi}{2}$ and $\pi$ in the Poincar\'e
sphere, as required for applications based on spin-polarisation mapping and
spin-mediated photon-photon gates. In agreement with our modeling, we observe
that the environmental noise does not limit the amplitude of the spin-induced
rotation, yet slightly degrades the polarisation purity of the output states.
We find that the polarisation state of the reflected photons can be manipulated
in most of the Poincar\'e sphere, through controlled spin-induced rotations,
thanks to moderate cavity birefringence and limited noise. This control allows
the operation of spin-photon interfaces in various configurations, including at
zero or low magnetic fields, which ensures compatibility with key protocols for
photonic cluster state generation.
