  Neutrino- and antineutrino-oxygen neutral-current quasielastic-like
interactions are measured at Super-Kamiokande using nuclear de-excitation
$\gamma$-rays to identify signal-like interactions in data from a $14.94 \
(16.35)\times 10^{20}$ protons-on-target exposure of the T2K neutrino
(antineutrino) beam. The measured flux-averaged cross sections on oxygen nuclei
are $\langle \sigma_{\nu {\rm -NCQE}} \rangle = 1.70 \pm 0.17 ({\rm stat.}) ^{+
{\rm 0.51}}_{- {\rm 0.38}} ({\rm syst.}) \times 10^{-38} \ {\rm cm^2/oxygen}$
with a flux-averaged energy of 0.82 GeV and $\langle \sigma_{\bar{\nu} {\rm
-NCQE}} \rangle = 0.98 \pm 0.16 ({\rm stat.}) ^{+ {\rm 0.26}}_{- {\rm 0.19}}
({\rm syst.}) \times 10^{-38} \ {\rm cm^2/oxygen}$ with a flux-averaged energy
of 0.68 GeV, for neutrinos and antineutrinos, respectively. These results are
the most precise to date, and the antineutrino result is the first cross
section measurement of this channel. They are compared with various theoretical
predictions. The impact on evaluation of backgrounds to searches for supernova
relic neutrinos at present and future water Cherenkov detectors is also
discussed.
