  In this paper we consider the coherence properties of neutrinos produced by
the decays of pions in conventional neutrino beams. Using a multi-particle
density matrix formalism we derive the oscillation probability for neutrinos
emitted by a decaying pion in an arbitrary quantum state. Then, using methods
from decoherence theory we calculate the pion state which evolves through
interaction with decay-pipe gases in a typical accelerator neutrino experiment.
These two ingredients are used to obtain the distance scales for neutrino beam
coherence loss. We find that for the known neutrino mass splittings, no
non-standard oscillation effects are expected on terrestrial baselines. Heavy
sterile neutrinos may experience terrestrial loss of coherence, and we
calculate both the distance over which this occurs and the energy resolution
required to observe the effect. By treating the pion-muon-neutrino-environment
system quantum mechanically, neutrino beam coherence properties are obtained
without assuming arbitrary spatial or temporal scales at the neutrino
production vertex.
