Deterministic Photonic Entanglement Arising from Non-Abelian Quantum Holonomy

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. Crucially, we generalize this approach to demonstrate the potentiality of deterministically entangling two arbitrarily high, N-dimensional quantum systems, by formally establishing a deep connection between the matrix representations of the unitary quantum holonomy-within energy-degenerate subspaces in which the total excitation number is conserved-and the (2j+1)-dimensional irreducible representations of the rotation operator, where j=(N-1)/2 and N≥2. Specifically, our protocol deterministically entangles spatially localized modes that are not only distinguishable but are also individually accessible and amenable to state preparation and measurement, and therefore, we envisage that this entangling mechanism could be utilized for deterministic quantum information processing with light.