Entanglement, Non-linear Dynamics, and the Heisenberg Limit

TL;DR

This paper establishes that quantum Fisher information can identify useful multi-particle entanglement for surpassing classical phase sensitivity limits, and explores generating such states via non-linear dynamics in Bose-Einstein condensates or trapped ions.

Contribution

It provides a criterion based on quantum Fisher information for recognizing useful entanglement and analyzes its creation through non-linear evolution in quantum systems.

Findings

Quantum Fisher information characterizes useful entanglement for quantum metrology.

Necessary and sufficient conditions for sub shot-noise sensitivity are derived.

Non-linear dynamics can generate entangled states that improve measurement precision.

Abstract

We show that the quantum Fisher information provides a sufficient condition to recognize multi-particle entanglement in a $N$ qubit state. The same criterion gives a necessary and sufficient condition for sub shot-noise phase sensitivity in the estimation of a collective rotation angle $\theta$. The analysis therefore singles out the class of entangled states which are {\it useful} to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the non-linear dynamical evolution of two decoupled Bose-Einstein condensates or trapped ions.