  It has long been recognized that the neutrinos detected from the next
core-collapse supernova in the Galaxy have the potential to reveal important
information about the dynamics of the explosion and the nucleosynthesis
conditions as well as allowing us to probe the properties of the neutrino
itself. The neutrinos emitted from thermonuclear - type Ia - supernovae also
possess the same potential, although these supernovae are dimmer neutrino
sources. For the first time, we calculate the time, energy, line of sight, and
neutrino-flavor-dependent features of the neutrino signal expected from a
three-dimensional delayed-detonation explosion simulation, where a
deflagration-to-detonation transition triggers the complete disruption of a
near-Chandrasekhar mass carbon-oxygen white dwarf. We also calculate the
neutrino flavor evolution along eight lines of sight through the simulation as
a function of time and energy using an exact three-flavor transformation code.
We identify a characteristic spectral peak at $\sim 10$ MeV as a signature of
electron captures on copper. This peak is a potentially distinguishing feature
of explosion models since it reflects the nucleosynthesis conditions early in
the explosion. We simulate the event rates in the Super-K, Hyper-K, JUNO, and
DUNE neutrino detectors with the SNOwGLoBES event rate calculation software and
also compute the IceCube signal. Hyper-K will be able to detect neutrinos from
our model out to a distance of $\sim 10$ kpc. At 1 kpc, JUNO, Super-K, and DUNE
would register a few events while IceCube and Hyper-K would register several
tens of events.
