Unscrambling entanglement through a complex medium

The transfer of quantum information through a noisy environment is a central challenge in the fields of quantum communication, imaging and nanophotonics. In particular, high-dimensional quantum states of light enable quantum networks with significantly higher information capacities and noise robustness as compared with qubits. However, although qubit entanglement has been distributed over large distances through free space and fibre, the transport of high-dimensional entanglement is hindered by the complexity of the channel, which encompasses effects such as free-space turbulence or mode mixing in multimode waveguides. Here, we demonstrate the transport of six-dimensional spatial-mode entanglement through a 2-m-long, commercial multimode fibre with 84.4% fidelity. We show how the entanglement can itself be used to measure the transmission matrix of the complex medium, allowing the recovery of quantum correlations that were initially lost. Using a unique property of entangled states, the medium is rendered transparent to entanglement by carefully 'scrambling' the photon that did not enter it, rather than unscrambling the photon that did. Our work overcomes a primary challenge in the fields of quantum communication and imaging, and opens a new pathway towards the control of complex scattering processes in the quantum regime. Higher-dimensional entanglement between two photons can be preserved for a photon passing through a complex medium by applying an appropriate scrambling operation on the entangled partner that does not enter the complex medium.