# Quantum sensing close to a dissipative phase transition: symmetry breaking and criticality as metrological resources

## TL;DR

This paper explores how a single qubit-laser can serve as an effective quantum sensor near a dissipative phase transition, leveraging symmetry breaking and criticality to enhance measurement precision.

## Contribution

It demonstrates that the lasing phase transition's critical point and symmetry breaking can be exploited for optimal quantum parameter estimation.

## Key findings

- Quantum Fisher information scales linearly with boson number.
- Optimal measurement occurs at the critical point of the phase transition.
- Increased incoherent pumping improves measurement precision.

## Abstract

We study the performance of a single qubit-laser as a quantum sensor to measure the amplitude and phase of a driving field. By using parameter estimation theory we show that certain suitable field quadratures are optimal observables in the lasing phase. The quantum Fisher information scales linearly with the number of bosons and thus the precision can be enhanced by increasing the incoherent pumping acting on the qubit. If we restrict ourselves to measurements of the boson number observable, then the optimal operating point is the critical point of the lasing phase transition. Our results point out to an intimate connection between symmetry breaking, dissipative phase transitions and efficient parameter estimation.