# Estimating phase with a random generator: Strategies and resources in multiparameter quantum metrology

## TL;DR

This paper investigates strategies for joint estimation of phase and noise parameters in quantum metrology, demonstrating that entanglement and optimized schemes can significantly improve precision with fewer resources, especially at moderate interaction counts.

## Contribution

It introduces new estimation strategies for phase and noise parameters in quantum metrology, showing that entanglement isn't always necessary for quantum advantage.

## Key findings

- Simultaneous estimation reduces resource requirements by up to twofold.
- Quantum enhancement is achievable at moderate number of interactions.
- Classical strategies dominate at large interaction counts, following the standard quantum limit.

## Abstract

Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $\varphi$ whose generator is randomly sampled according to a distribution with unknown concentration $\kappa$, which introduces a physical source of noise. We then investigate strategies for the joint estimation of the two parameters $\varphi$ and $\kappa$ given a finite number $N$ of interactions with the phase imprinting channel. We consider both single qubit and multipartite entangled probes, and identify regions of the parameters where simultaneous estimation is advantageous, resulting in up to a twofold reduction in resources. Quantum enhanced precision is achievable at moderate $N$, while for sufficiently large $N$ classical strategies take over and the precision follows the standard quantum limit. We show that full-scale entanglement is not needed to reach such an enhancement, as efficient strategies using significantly fewer qubits in a scheme interpolating between the conventional sequential and parallel metrological schemes yield the same effective performance. These results may have relevant applications in optimization of sensing technologies.