Quantum enhanced estimation of a multi-dimensional field

TL;DR

This paper introduces a quantum framework for simultaneously estimating multiple non-commuting parameters, such as magnetic field components, using entangled probe states that outperform traditional methods, while highlighting the nuanced role of entanglement.

Contribution

It develops a formalism for multi-parameter quantum estimation, proposes a superior probe state, and analyzes the impact of entanglement on precision scaling.

Findings

Proposed a probe state surpassing individual component estimation precision.

Identified measurement strategies approaching the quantum limit.

Discovered excessive entanglement can hinder Heisenberg scaling.

Abstract

We present a framework for the quantum enhanced estimation of multiple parameters corresponding to non-commuting unitary generators. Our formalism provides a recipe for the simultaneous estimation of all three components of a magnetic field. We propose a probe state that surpasses the precision of estimating the three components individually and discuss measurements that come close to attaining the quantum limit. Our study also reveals that too much quantum entanglement may be detrimental to attaining the Heisenberg scaling in quantum metrology.