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.

• Received 2 February 2021
• Accepted 30 June 2021

DOI:https://doi.org/10.1103/PhysRevA.104.012607