  Minimizing both experimental effort and consumption of valuable quantum
resources in state estimation is vital in practical quantum information
processing. Here, we explore characterizing states as an additional benefit of
the entanglement distillation protocols. We show that the Bell-diagonal
parameters of any undistilled state can be efficiently estimated solely from
the measurement statistics of probabilistic distillation protocols. We further
introduce the state estimator `Disti-Mator' designed specifically for a
realistic experimental setting, and exhibit its robustness through numerical
simulations. Our results demonstrate that a separate estimation protocol can be
circumvented whenever distillation is an indispensable communication-based
task.
