Spin squeezing inequalities for arbitrary spin

TL;DR

This paper derives comprehensive spin squeezing inequalities for particles of any spin, enabling experimental detection of entanglement in ensembles without individual particle access, and introduces criteria for various types of entanglement.

Contribution

It provides a complete set of generalized spin squeezing inequalities for arbitrary spin particles, expanding tools for entanglement detection in collective measurements.

Findings

Inequalities can detect k-particle entanglement.

Some criteria identify bound entanglement.

Applicable to experimental setups with collective observables.

Abstract

We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement.