  The complementarity between the quark and lepton mixing matrices is shown to
provide robust predictions. We obtain these predictions by first showing that
the matrix V_M, product of the quark (CKM) and lepton (PMNS) mixing matrices,
may have a zero (1,3) entry which is favored by experimental data.
  We obtain that any theoretical model with a vanishing (1,3) entry of V_M that
is in agreement with quark data, solar, and atmospheric mixing angle leads to
$\theta_{13}^{PMNS}=(9{^{+1}_{-2}})^\circ$. This value is consistent with the
present 90% CL experimental upper limit. We also investigate the prediction on
the lepton phases. We show that the actual evidence, under the only assumption
that the correlation matrix V_M product of CKM and PMNS has a zero in the entry
(1,3), gives us a prediction for the three CP-violating invariants J, S_1, and
S_2. A better determination of the lepton mixing angles will give stronger
prediction for the CP-violating invariants in the lepton sector. These will be
tested in the next generation experiments. Finally we compute the effect of non
diagonal neutrino mass in "l_i -> l_j gamma" in SUSY theories with non trivial
Quark-Lepton complementarity and a flavor symmetry. The Quark-Lepton
complementarity and the flavor symmetry strongly constrain the theory and we
obtain a clear prediction for the contribution to "mu -> e gamma" and the "tau"
decays "tau -> e gamma" and "tau -> mu gamma". If the Dirac neutrino Yukawa
couplings are degenerate but the low energy neutrino masses are not degenerate,
then the lepton decays are related among them by the V_M entries. On the other
hand, if the Dirac neutrino Yukawa couplings are hierarchical or the low energy
neutrino masses are degenerate, then the prediction for the lepton decays comes
from the CKM hierarchy.
