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, while 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 multi-mode waveguides. Here we demonstrate the transport of six-dimensional spatial-mode entanglement through a two-metre long, commercial multi-mode 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.

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