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Protecting weak measurements against systematic errors

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Decoherence in quantum metrology may deviate the estimate of a parameter from the real value of the parameter. In this talk, we show how to suppress the systematic error of weak-measurement-based quantum metrology under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first order approximation of a small deviation in the probability distribution, and compare the systematic error of standard weak measurement and postselected weak measurements, which shows that the systematic error of a postselected weak measurement with a large weak value can be significantly lower than that of a standard weak measurement when the probe undergoes decoherence.