  Realizing deterministic, high-fidelity entangling interactions--of the kind
that can be utilized for efficient quantum information processing--between
photons remains an elusive goal. Here, we address this long-standing issue by
devising a protocol for creating and manipulating highly-entangled
superpositions of well-controlled states of light by using an on-chip photonic
system that has recently been shown to implement three-dimensional, non-Abelian
quantum holonomy. Our calculations indicate that a subset of such entangled
superpositions are maximally-entangled, volume-law states, and that the
underlying entanglement can be distilled and purified for applications in
quantum science. Specifically, we envisage that this entangling mechanism could
be utilized for realizing two-qubit, universal, entangling quantum gates with
linear photonic elements alone. Furthermore, this method should also--at least,
in principle--be generalizable to systems of neutral atoms.
