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Weak value amplification and other postselection-based metrological protocols can enhance precision while estimating small parameters, outperforming postselection-free protocols. In general, these enhancements are largely constrained because the protocols yielding higher precision are rarely obtained due to a lower probability of successful postselection. It is shown that this precision can further be improved with the help of quantum resources like entanglement and negativity in the quasiprobability distribution. However, these quantum advantages in attaining considerable success probability with large precision are bounded irrespective of any accessible quantum resources. We derive a bound of these advantages in postselected metrology, establishing a connection with weak value optimization where the latter can be understood in terms of geometric phase. We introduce a scheme that saturates the bound, yielding anomalously large precision. Usually, negative quasiprobabilities are considered essential in enabling postselection to increase precision beyond standard optimized values. In contrast, we prove that these advantages can indeed be achieved with positive quasiprobability distribution. For that, we construct a metrological procedure using a three-level non-degenerate quantum system.
Zoom Link: https://cern.zoom.us/j/67733971295?pwd=aUE4Q3lBeVhlU1A3eFBkdm5ucXRuUT09
Meeting ID: 677 3397 1295 Password: 123456