  Neutrino oscillation represents an intriguing physical phenomenon where the
quantumness can be maintained and detected over a long distance. Previously,
the non-classical character of neutrino oscillation was tested with the
Leggett-Garg inequality, where a clear violation of the classical bound was
observed [J. A. Formaggio et al., Phys. Rev. Lett. 117, 050402 (2016)].
However, there are several limitations in testing neutrino oscillations with
the Leggett-Garg inequality. In particular, the degree of violation of the
Leggett-Garg inequality cannot be taken as a "measure of quantumness". Here we
focus on quantifying the quantumness of experimentally-observed neutrino
oscillation, using the tools of recently-developed quantum resource theory. We
analyzed ensembles of reactor and accelerator neutrinos at distinct energies
from a variety of neutrino sources, including Daya Bay (0.5 km and 1.6 km),
Kamland (180 km), MINOS (735 km), and T2K (295 km). The quantumness of the
three-flavoured neutrino oscillation is characterized within a 3{\sigma} range
relative to the theoretical prediction. It is found that the maximal coherence
was observed in the neutrino source from the Kamland reactor. However, even
though the survival probability of the Daya Bay experiment did not vary
significantly (dropped about 10 percent), the coherence recorded can reach up
to 40 percent of the maximal value. These results represent the longest
distance over which quantumness were experimentally determined for quantum
particles other than photons.
