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In quantum precision metrology, the famous result of Heisenberg limit scalingas $1/N$ (with $N$ the number of probes) can be surpassed by consideringnonlinear coupling measurement. In this work, we consider the mostpractice-relevant quadratic nonlinear coupling and show that the metrologicalprecision can be enhanced from the $1/N^{\frac{3}{2}}$ super-Heisenberg scalingto $1/N^2$, by simply employing a pre- and post-selection (PPS) technique, butnot using any expensive quantum resources such as quantum entangled state ofprobes.

Enhanced super-Heisenberg scaling precision by nonlinear coupling and postselection