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The large number of spatial modes supported by standard multimode fibers is apromising platform for boosting the channel capacity of quantum and classicalcommunications by orders of magnitude. However, the practical use of longmultimode fibers is severely hampered by modal crosstalk and polarizationmixing. To overcome these challenges, we develop and experimentally demonstratea vectorial time reversal technique, which is accomplished by digitallypre-shaping the wavefront and polarization of the forward-propagating signalbeam to be the phase conjugate of an auxiliary, backward-propagating probebeam. Here, we report an average modal fidelity above 80% for 210Laguerre-Gauss and Hermite-Gauss modes by using vectorial time reversal over anunstabilized 1-km-long fiber. We also propose a practical and scalablespatial-mode-multiplexed quantum communication protocol over long multimodefibers to illustrate potential applications that can be enabled by ourtechnique.

High-fidelity spatial mode transmission through a 1-km-long multimode fiber via vectorial time reversal