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The orbital angular momentum (OAM) of photons presents a degree of freedomfor enhancing the secure key rate of free-space quantum key distribution (QKD)through mode-division multiplexing (MDM). However, atmospheric turbulence canlead to substantial modal crosstalk, which is a long-standing challenge to MDMfor free-space QKD. Here, we show that the digital generation of time-reversedwavefronts for multiple probe beams is an effective method for mitigatingatmospheric turbulence. We experimentally characterize seven OAM modes afterpropagation through a 340-m outdoor free-space link and observe an averagemodal crosstalk as low as 13.2% by implementing real-time time reversal. Thecrosstalk can be further reduced to 3.4% when adopting a mode spacing $\Delta\ell$ of 2. We implement a classical MDM system as a proof-of-principledemonstration, and the bit error rate is reduced from $3.6\times 10^{-3}$ to beless than $1.3\times 10^{-7}$ through the use of time reversal. We also proposea practical and scalable scheme for high-speed, mode-multiplexed QKD through aturbulent link. The modal crosstalk can be further reduced by using fasterequipment. Our method can be useful to various free-space applications thatrequire crosstalk suppression.

Multiprobe time reversal for high-fidelity vortex-mode-division multiplexing over a turbulent free-space link