Overcoming wavelength-dependent nonreciprocity using superimposed quantum two-way time transfer

Quantum two-way time transfer (Q-TWTT) is fundamentally limited by wavelength-dependent nonreciprocity between counter-propagating photons, which induces undesired time-offset drifts and compromises its long-term stability. To overcome this bottleneck, we propose and experimentally validate a superimposed Q-TWTT (SQ-TWTT) protocol. By shifting the transmission scheme from bidirectional single-photon exchange to concurrent streams of photon pairs, SQ-TWTT confers robust immunity to nonreciprocal delays. Comparative tests conducted over a 113 km fiber link revealed a fundamental divergence in performance. Whereas conventional Q-TWTT exhibited a time-offset drift that scaled proportionally with both the photon wavelength difference and the link dispersion, the SQ-TWTT protocol maintained negligible sensitivity to these nonreciprocal effects. Over a wavelength mismatch range from 0 to 4.64 nm, the time-offset in conventional Q-TWTT accumulated dramatically to ($164.35~\pm~2.65$) ps. In stark contrast, SQ-TWTT sustained a negligible drift of ($0.07~\pm~1.94$) ps over the same range. These results, in excellent agreement with theory, confirm that SQ-TWTT breaks the long-standing limitation of Q-TWTT and establishes a practical, high-precision solution for long-distance time synchronization in fiber-optic networks.