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The recently proposed phase-matching quantum key distribution offers means to overcome the linear key rate–transmittance bound. Since the key information is encoded onto the phases of coherent states, the misalignment between the two remote reference frames would yield errors and significantly degrade the key generation rate from the ideal case. In this work, we propose a reference-frame-independent design of phase-matching quantum key distribution by introducing a high-dimensional key encodingdoi:10.17863/cam.75480 fatcat:tois5or4nndvdl3a4n3qpyxvwi