The multimode nature of photons generated in parametric down-conversion has inspired a generation of experiments on high-dimensional entanglement, ranging from complete quantum state teleportation to exotic multipartite entanglement. Photons entangled in their position-momentum degrees of freedom serve as an elegant manifestation of the Einstein-Podolsky-Rosen paradox, while also enhancing quantum technologies for communication, imaging, and computation. This work paves the way toward manipulation and transport of entanglement through scattering media, with potential applications in quantum microscopy and quantum key distribution. Furthermore, we certify an entanglement dimensionality of 17. Through violation of an Einstein-Podolski-Rosen criterion by 988σ, we show the presence of entanglement after the medium.

Using a transmission matrix approach, we perform wave-front correction in the classical domain using an intense classical beam as a beacon to compensate for the disturbances suffered by a copropagating beam of entangled photons. Here, we demonstrate a wavefront shaping approach to transmit high-dimensional spatially entangled photon pairs through scattering media. However, the presence of optical disorder such as atmospheric turbulence or biological tissue perturbs quantum state propagation and hinders their practical use.

In particular, they enable quantum communications with higher information capacities or enhanced imaging protocols. High-dimensional entangled quantum states improve the performance of quantum technologies compared to qubit-based approaches.

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