Rapid and efficient wavefront correction for spatially entangled photons using symmetrized optimization

Spatial entanglement is a key resource in quantum technologies, enabling applications in quantum communication, imaging, and computation. However, propagation through complex media distorts spatial correlation, posing a challenge for practical implementations. We introduce a symmetrized genetic algorithm (sGA) for adaptive wavefront correction of spatially entangled photons, leveraging the insight that only the even-parity component of wavefront distortions affects two-photon correlation. By enforcing symmetry constraints, sGA reduces the optimization parameter space by half, leading to faster convergence and improved enhancement within a finite number of generations compared to standard genetic algorithms. In addition, we establish the dependence of enhancement on the signal-to-noise ratio of the feedback signal, which is controlled by detector integration time. This technique enables correction of entanglement degradation, enhancing quantum imaging, secure quantum communication, and quantum sensing in complex environments.