In quantum precision metrology, the famous result of Heisenberg limit scaling
as 1/N (with N the number of probes) can be surpassed by considering
nonlinear coupling measurement. In this work, we consider the most
practice-relevant quadratic nonlinear coupling and show that the metrological
precision can be enhanced from the 1/N23​ super-Heisenberg scaling
to 1/N2, by simply employing a pre- and post-selection (PPS) technique, but
not using any expensive quantum resources such as quantum entangled state of
probes.Comment: 6 pages, 4 figure