Wavefront correction of high-dimensional two-photon states via coherence-entanglement transfer

Reliable transmission of quantum optical states through real-world environments is key for quantum communication and imaging. Yet, aberrations and scattering in the propagation path can scramble the transmitted signal and hinder its use. A typical strategy is to employ a classical beacon beam to learn and then correct for the wavefront distortions. However, relying on a separate light source increases the overhead in the experimental apparatus. Moreover, the beacon light must closely match the non-classical state in polarization, wavelength, and even temporal bandwidth, which is highly challenging in practice. Here, we introduce a fast and efficient wavefront correction approach where we use the quantum state itself to correct for optical distortion. Via pump shaping, we control the degree of entanglement in the spatially-entangled two-photon state so that it behaves either as a high-dimensional entangled state or as a classical coherent state. The latter case is used to efficiently measure the transmission matrix of the propagation channel and correct its distortions with a spatial light modulator, thereby enabling the transmission of the high-dimensional entangled state with minimal errors. Our approach paves the way for the practical implementation of quantum imaging and communication protocols based on high-dimensional spatially entangled states.