Enhanced super-Heisenberg scaling precision by nonlinear coupling and postselection

TL;DR

This paper demonstrates that using quadratic nonlinear coupling and postselection techniques in quantum metrology can significantly surpass the Heisenberg limit, achieving a $1/N^2$ scaling without requiring entangled probes.

Contribution

The study introduces a practical method to enhance quantum measurement precision beyond super-Heisenberg limits using simple postselection, without entanglement.

Findings

Achieves $1/N^2$ scaling in precision.

Enhancement from $1/N^{3/2}$ to $1/N^2$ with quadratic nonlinear coupling.

No need for entangled quantum resources.

Abstract

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