The Influence of Quantum Correlation on the Holonomy of Spatially-Structured Bi-Photons

The manifestation of entanglement within geometric phase is elucidated for spatially-structured bi-photons. Entanglement parameters are shown to influence holonomy in two distinct ways: through statistical superpositions of separable states; and via quantum correlation. These are entwined within geometric phase, motivating the construction of a projective, gauge-invariant measure that allows the manifestation of quantum correlation to be pinpointed and explained. An optical circuit consisting of a pair of misoriented mode converters gives a practical demonstration. This is facilitated by a novel pump engineering method which produces photon pairs with tunable entanglement.