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-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVMhas an equivalent minimal sufficient POVMand 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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics