  A key ingredient in emerging quantum-enhanced technologies is the ability to
coherently manipulate and detect superpositions of basis states. In integrated
optics implementations, transverse spatial modes supported by multimode
structures offer an attractive carrier of quantum superpositions. Here we
propose an integrated dynamic mode converter based on the electro-optic effect
in nonlinear channel waveguides for deterministic transformations between
mutually non-orthogonal bases of spatial modes. We theoretically show its
capability to demonstrate a violation of a Bell-type Clauser-Horne-Shimony-Holt
inequality by measuring spatially mode-entangled photon pairs generated by an
integrated photon pair source. The proposed configuration, numerically studied
for the potassium titanyl phosphate (KTP) material, can be easily implemented
using standard integrated optical fabrication technology.
