  Phase manipulation is essential to quantum information processing, for which
the orbital angular momentum (OAM) of photon is a promising high-dimensional
resource. Dove prism (DP) is one of the most important element to realize the
nondestructive phase manipulation of OAM photons. DP usually changes the
polarization of light and thus increases the manipulation error for a spin-OAM
hybrid state. DP in a Sagnac interferometer also introduces a mode-dependent
global phase to the OAM mode. In this work, we implemented a high-dimensional
controlled-phase manipulation module (PMM), which can compensate the
mode-dependent global phase and thus preserve the phase in the spin-OAM hybrid
superposition state. The PMM is stable for free running and is suitable to
realize the high-dimensional controlled-phase gate for spin-OAM hybrid states.
Considering the Sagnac-based structure, the PMM is also suitable for classical
communication with spin-OAM hybrid light field.
