Fisher information and multiparticle entanglement

TL;DR

This paper establishes bounds on Fisher information for different multiparticle entanglement classes, demonstrating that genuine multiparticle entanglement is essential for optimal quantum interferometry sensitivity.

Contribution

It derives bounds on Fisher information for various entanglement classes and introduces criteria that detect different entangled states, including bound entangled states.

Findings

Genuine multiparticle entanglement is necessary for high sensitivity in quantum interferometry.

Bounds on Fisher information distinguish different entanglement classes.

The criteria can detect bound entangled states using experimental data.

Abstract

The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on $F$ for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information $\bar F$ for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on $\bar F$ is able to detect certain bound entangled states.