# Limited-control metrology approaching the Heisenberg limit without entanglement preparation

## TL;DR

This paper demonstrates that limited control in quantum metrology can still achieve near-Heisenberg precision scaling, approaching the performance of fully controlled systems without requiring entanglement.

## Contribution

It introduces a protocol for magnetic field measurement with limited control, achieving super-Heisenberg scaling and near-optimal precision without entanglement preparation.

## Key findings

- Achieves transient super-Heisenberg scaling in measurement time.
- Reaches Heisenberg scaling in particle number.
- Estimates uncertainty close to fully controlled systems within a constant factor.

## Abstract

Current metrological bounds typically assume full control over all particles that are involved in the protocol. Relaxing this assumption we study metrological performance when only limited control is available. As an example, we measure a static magnetic field when a fully controlled quantum sensor is supplemented by particles over which only global control is possible. We show that even for a noisy quantum sensor, a protocol that maps the magnetic field to a precession frequency can achieve transient super-Heisenberg scaling in measurement time and Heisenberg scaling in the particle number. This leads to an estimation uncertainty that approaches that achievable under full control to within a factor independent of the particle number for a given total time. Applications to hybrid sensing devices and the crucial role of the quantum character of the sensor are discussed.