  IceCube, a future km^3 antarctic ice Cherenkov neutrino telescope, is highly
sensitive to a galactic supernova (SN) neutrino burst. The Cherenkov light
corresponding to the total energy deposited by the SN neutrinos in the ice can
be measured relative to background fluctuations with a statistical precision
much better than 1%. If the SN is viewed through the Earth, the matter effect
on neutrino oscillations can change the signal by more than 5%, depending on
the flavor-dependent source spectra and the neutrino mixing parameters.
Therefore, IceCube together with another high-statistics experiment like
Hyper-Kamiokande can detect the Earth effect, an observation that would
identify specific neutrino mixing scenarios that are difficult to pin down with
long-baseline experiments. In particular, the normal mass hierarchy can be
clearly detected if the third mixing angle is not too small, sin^2 theta_13 <
10^-3. The small flavor-dependent differences of the SN neutrino fluxes and
spectra that are found in state-of-the-art simulations suffice for this
purpose. Although the absolute calibration uncertainty at IceCube may exceed
5%, the Earth effect would typically vary by a large amount over the duration
of the SN signal, obviating the need for a precise calibration. Therefore,
IceCube with its unique geographic location and expected longevity can play a
decisive role as a "co-detector" to measure SN neutrino oscillations. It is
also a powerful stand-alone SN detector that can verify the delayed-explosion
scenario.
