Entanglement and extreme spin squeezing of unpolarized states

TL;DR

This paper introduces new criteria for detecting entanglement depth in unpolarized spin states, including Dicke states, using variance and moments, which are practical and outperform previous methods especially under noise.

Contribution

The authors develop easy-to-evaluate criteria for entanglement detection in unpolarized states, extending spin squeezing concepts to Dicke states and systems with particle number fluctuations.

Findings

Criteria outperform past approaches in noisy conditions

Analytic bounds enable spin-squeezing parameters for Dicke states

Extension to systems with fluctuating particle numbers

Abstract

We present criteria to detect the depth of entanglement in macroscopic ensembles of spin-j particles using the variance and second moments of the collective spin components. The class of states detected goes beyond traditional spin-squeezed states by including Dicke states and other unpolarized states. The criteria derived are easy to evaluate numerically even for systems of very many particles and outperform past approaches, especially in practical situations where noise is present. We also derive analytic lower bounds based on the linearization of our criteria, which make it possible to define spin-squeezing parameters for Dicke states. In addition, we obtain spin squeezing parameters also from the condition derived in [A. S. Sorensen and K. Molmer, Phys. Rev. Lett. 86, 4431 (2001)]. We also extend our results to systems with fluctuating number of particles.