  For neutrino oscillations to take place the entangled quantum state of a
neutrino and a charged lepton produced via charged current interactions must be
disentangled. Implementing a non-perturbative Wigner-Weisskopf method we obtain
the correct \emph{entangled} quantum state of neutrinos and charged leptons
from the (two-body) decay of a parent particle. The source lifetime and
disentanglement length scale lead to a suppression of the oscillation
probabilities in short-baseline experiments. The suppression is determined by
$\pi\, L_s/L_{osc}$ where $L_s$ is the \emph{smallest} of the decay length of
the parent particle or the disentanglement length scale. For $L_s \geq L_{osc}$
coherence and oscillations are suppressed. These effects are more prominent in
\emph{short base line experiments} and at low neutrino energy. We obtain the
corrections to the appearance and disappearance probabilities modified by both
the lifetime of the source and the disentanglement scale and discuss their
implications for accelerator and reactor experiments. These effects imply that
fits to the experimental data based on the usual quantum mechanical formulation
\emph{underestimate} $\sin^2(2\theta)$ and $\delta m^2$, and are more dramatic
for $\delta m^2\simeq \,\mathrm{eV}^2$, the mass range for new generations of
sterile neutrinos that could explain the short-baseline anomalies.
