  We show that measurement incompatibility is a necessary resource to enhance
the precision of quantum metrology. To utilize incompatible measurements, we
propose a probabilistic method of operational quasiprobability (OQ) consisting
of the measuring averages. OQ becomes positive semidefinite for some quantum
states. We prove that Fisher information (FI), based on positive OQ, can be
larger than the conventional quantum FI. Applying the proof, we show that FI of
OQ can be extremely larger than quantum FI, when estimating a parameter encoded
onto a qubit state with two mutually unbiased measurements. By adopting maximum
likelihood estimator and linear error propagation methods, we illustrate that
they achieve the high precision that our model predicts. This approach is
expected to be applicable to improve quantum sensors.
