  As a result of a non-trivial mixing matrix, neutrinos cannot be
simultaneously in a flavor and mass eigenstate. We formulate and discuss
information entropic relations that quantify the associated quantum
uncertainty. We also formulate a protocol to determine the
Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and
measurements on an entangled lepton-neutrino pair. The entangled state features
neutrino oscillations in a conditional probability involving measurements on
the lepton and the neutrino. They can be switched off by choosing a specific
observable on the lepton side which is determined by the PMNS matrix. The
parameters of the latter, including the CP-violating phase $\delta$, can be
obtained by guessing them and improving the guess by minimizing the remaining
oscillations.
