  Rotating and magnetized protoneutron stars (PNSs) may drive relativistic
magneto-centrifugally accelerated winds as they cool immediately after core
collapse. The wind fluid near the star is composed of neutrons and protons, and
the neutrons become relativistic while collisionally coupled with the ions.
Here, we argue that the neutrons in the flow eventually undergo inelastic
collisions around the termination shock inside the stellar material, producing
~0.1-1 GeV neutrinos, without relying on cosmic-ray acceleration mechanisms.
Even higher-energy neutrinos may be produced via particle acceleration
mechanisms. We show that PINGU and Hyper-Kamiokande can detect such neutrinos
from nearby core-collapse supernovae, by reducing the atmospheric neutrino
background via coincident detection of MeV neutrinos or gravitational waves and
optical observations. Detection of these GeV and/or higher-energy neutrinos
would provide important clues to the physics of magnetic acceleration,
nucleosynthesis, the relation between supernovae and gamma-ray bursts, and the
properties of newly born neutron stars.
