  Multiparameter quantum estimation is made difficult by the following three
obstacles. First, incompatibility among different physical quantities poses a
limit on the attainable precision. Second, the ultimate precision is not
saturated until you discover the optimal measurement. Third, the optimal
measurement may generally depend on the target values of parameters, and thus
may be impossible to perform for unknown target states.
  We present a method to circumvent these three obstacles. A class of quantum
statistical models, which utilizes antiunitary symmetries or, equivalently,
real density matrices, offers compatible multiparameter estimations. The
symmetries accompany the target-independent optimal measurements for pure-state
models. Based on this finding, we propose methods to implement antiunitary
symmetries for quantum metrology schemes. We further introduce a function which
measures antiunitary asymmetry of quantum statistical models as a potential
tool to characterize quantumness of phase transitions.
