Precision Limits in Quantum Metrology with Open Quantum Systems

TL;DR

This paper reviews recent theoretical advances in quantum metrology, demonstrating that quantum advantages in measurement precision can persist despite environmental noise, by analyzing quantum dynamical maps and microscopic dissipative models.

Contribution

It introduces a framework combining quantum dynamical maps and microscopic models to establish precision bounds in noisy quantum metrology, highlighting conditions for surpassing classical limits.

Findings

Quantum noise can still allow precision beyond classical bounds.

Environmental fluctuations do not always limit quantum measurement advantages.

A unified approach links abstract formalism to microscopic dissipative dynamics.

Abstract

The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcome when using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining general precision bounds in the presence of an environment. We adopt a complementary approach, where we first analyze the problem within the general framework of describing the quantum systems in terms of quantum dynamical maps and then relate this abstract formalism to a microscopic description of the system's dissipative time evolution. We will show that although some forms of noise do render quantum systems standard quantum limited, precision beyond classical bounds is still possible in the presence of different forms of local environmental fluctuations.