IMSc Webinar

Bounding quantum advantages in Postselected Metrology

Subhrajit Modak

IISER -- Mohali

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. Here 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. We also
provide an optimal metrological scheme using three level non-degenerate
quantum system.