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We show that measurement incompatibility is a necessary resource to enhancethe precision of quantum metrology. To utilize incompatible measurements, wepropose a probabilistic method of operational quasiprobability (OQ) consistingof the measuring averages. OQ becomes positive semidefinite for some quantumstates. We prove that Fisher information (FI), based on positive OQ, can belarger than the conventional quantum FI. Applying the proof, we show that FI ofOQ can be extremely larger than quantum FI, when estimating a parameter encodedonto a qubit state with two mutually unbiased measurements. By adopting maximumlikelihood estimator and linear error propagation methods, we illustrate thatthey achieve the high precision that our model predicts. This approach isexpected to be applicable to improve quantum sensors.

Metrological power of incompatible measurements