Enhanced super-Heisenberg scaling precision by nonlinear coupling and postselection

In quantum precision metrology, the famous result of Heisenberg limit scaling as $1\mathrm{/}N$ (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 $1\mathrm{/}{N}^{\frac{3}{2}}$ super-Heisenberg scaling to $1\mathrm{/}{N}^2$, by simply employing a pre- and post-selection (PPS) technique, but not using any expensive quantum resources such as quantum entangled state of probes.