Entanglement witnesses based on first and second moments exist in the form of spin-squeezing criteria for the detection of particle entanglement from collective measurements, and in form of modified uncertainty relations for the detection of mode entanglement or steering. By revealing a correspondence between them, we show that metrologically useful spin squeezing reveals multimode entanglement in symmetric spin states that are distributed into addressable modes. We further derive tight state-independent multipartite entanglement bounds on the spin-squeezing coefficient and point out their connection to widely-used entanglement criteria that depend on the state's polarization. Our results are relevant for state-of-the-art experiments where symmetric entangled states are distributed into a number of addressable modes, such as split spin-squeezed Bose-Einstein condensates.
@article{arxiv.2004.01591,
title = {Relating spin squeezing to multipartite entanglement criteria for particles and modes},
author = {Matteo Fadel and Manuel Gessner},
journal= {arXiv preprint arXiv:2004.01591},
year = {2022}
}