  We introduce a concept of a minimal sufficient positive-operator valued
measure (POVM), which is the least redundant POVM among the POVMs that have the
equivalent information about the measured quantum system. Assuming the system
Hilbert space to be separable, we show that for a given POVM a sufficient
statistic called a Lehmann-Scheff\'{e}-Bahadur statistic induces a minimal
sufficient POVM. We also show that every POVM has an equivalent minimal
sufficient POVM and that such a minimal sufficient POVM is unique up to
relabeling neglecting null sets. We apply these results to discrete POVMs and
information conservation conditions proposed by the author.
