Quantum metrology from a quantum information science perspective

TL;DR

This paper reviews recent advances in quantum metrology, emphasizing the role of entanglement, fundamental concepts like quantum Fisher information, and the impact of noise on measurement precision.

Contribution

It provides a comprehensive overview of quantum metrology from a quantum information perspective, connecting theoretical principles with experimental implementations.

Findings

Entanglement is essential to surpass shot-noise scaling.

Quantum Fisher information relates to quantum state properties and evolution speed.

Noise imposes fundamental limits on measurement precision.

Abstract

We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger-Horne-Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer-Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks.