Geometric aspects of quantum theory provide deep, fundamental intimations of how to eventually reconcile quantum phenomena with gravitational effects. On the other hand, controllable, deterministic, multi-particle entanglement is the source of almost all advantages of quantum information processing systems over their classical counterparts. Recently, we have shown a new way of deterministically entangling two quantum-mechanical subsystems comprising optical photons. Our protocol is deterministic, since it makes use of unitary quantum evolution and does not require quantum measurements, which are inescapably probabilistic. To entangle photons without uncertainties, we have utilized a deep connection between quantum mechanics and differential geometry. In particular, we have shown that optical waveguides can be coupled in such a way that they synthesize a mathematical structure known as a non-Abelian (matrix-valued) holonomy, which—by utilizing the principles of conservation of total photon number and superposition of probability amplitudes—deterministically entangles photons that are incident on these waveguides