Relativistic Quantum Metrology in Open System Dynamics

TL;DR

This paper explores the ultimate precision limits of estimating the Unruh temperature using a two-level atom as a quantum detector in open system dynamics, demonstrating that population measurements can achieve quantum Fisher information bounds.

Contribution

It introduces a method to optimize quantum parameter estimation in open systems and shows population measurements can reach the quantum Fisher information limit.

Findings

Optimal estimation occurs with long evolution times.

Population measurement achieves the quantum Fisher information.

The method confirms the ultimate precision bound in quantum metrology.

Abstract

Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself.