Quantum metrology with precision reaching beyond-$1/N$ scaling through $N$-probe entanglement generating interactions

TL;DR

This paper proposes a quantum metrology method utilizing nonlinear interactions and $N$-probe entanglement to achieve precision scaling beyond the standard Heisenberg limit, with broad experimental applicability.

Contribution

It introduces a new nonlinear interaction-based measurement scheme that enhances precision scaling beyond $1/N$, adaptable to various physical measurements.

Findings

Achieves precision scaling of $D^{-N}/(N-1)!$ with $D > 2$

Applicable to measurements of gravity, magnetic fields, and gradients

Feasible implementation across multiple experimental platforms

Abstract

Nonlinear interactions are recognized as potential resources for quantum metrology, facilitating parameter estimation precisions that scale as the exponential Heisenberg limit of $2^{-N}$. We explore such nonlinearity and propose an associated quantum measurement scenario based on the nonlinear interaction of $N$-probe entanglement generating form. This scenario provides an enhanced precision scaling of $D^{-N}/(N-1)!$ with $D > 2$ a tunable parameter. In addition, it can be readily implemented in a variety of experimental platforms and applied to measurements of a wide range of quantities, including local gravitational acceleration $g$, magnetic field, and its higher-order gradients.