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The application of postselection to a weak quantum measurement leads to thephenomenon of weak values. Expressed in units of the measurement strength, thedisplacement of a quantum coherent measuring device is ordinarily bounded bythe eigenspectrum of the measured observable. Postselection can enable aninterference effect that moves the average displacement far outside this range,bringing practical benefits in certain situations. Employing the Fisherinformation metric, we argue that the amplified displacement offers nofundamental metrological advantage, due to the necessarily reduced probabilityof success. Our understanding of metrological advantage is the possibility of alower uncertainty in the estimate of an unknown parameter with a large numberof trials. We analyze a situation in which the detector is pixelated with afinite resolution, and in which the detector is afflicted by randomdisplacements: imperfections which degrade the fundamental limits of parameterestimation. Surprisingly, weak-value amplification is no more robust to themthan a technique making no use of the amplification effect brought about by afinal, postselected measurement.

When amplification with weak values fails to suppress technical noise