Reference-Frame-Independent Design of Phase-Matching Quantum Key Distribution

The recently proposed phase-matching quantum key distribution offers means to overcome the linear rate-transmittance bound. Since information is encoded onto phases of coherent states, misalignment between two remote reference frames would yield errors and significantly degrade generation rate from ideal case. In this work, we propose a reference-frame-independent design by introducing high-dimensional encoding space. With spanning unit circle, error statistics at arbitrary fixed phase difference can be recovered treated separately, which angle identified. By naturally extending binary symmetry complementarity high dimensions, present security proof demonstrate with simulation that 17-dimensional protocol completely immune any degree robust slow fluctuations. We expect practical for general phase-encoding schemes where relatively easy implement.