  Developing quantum networks necessitates coherently connecting distant
systems via remote strong coupling. Here, we demonstrate long-distance
coherence in cavity magnonics operating in the linear regime. By locally
setting the cavity near critical coupling with travelling photons, non-local
magnon-photon coherence is established via strong coupling over a 2-meter
distance. We observe two anomalies in this long-distance coherence: first, the
coupling strength oscillates twice the period of conventional photon-mediated
couplings; second, clear mode splitting is observed within the cavity
linewidth. Both effects cannot be explained by conventional coupled-mode
theory, which reveal the tip of an iceberg of photon-mediated coupling in
systems under critical driving. Our work shows the potential of using critical
phenomena for harnessing long-distance coherence in distributed systems.
