We show that collective three-body interactions (3BIs), implementable with N atoms loaded inside an optical cavity, offer a significant advantage for preparing complex multipartite entangled states. Firstly, they enable a speedup of order ∼N in preparing generalized Greenberger-Horne-Zeilinger (GHZ) states, outperforming conventional methods based on all-to-all two-body Ising interactions. Secondly, they saturate the Heisenberg bound in phase estimation tasks using a time-reversal protocol realized through simple rotations and followed by experimentally accessible collective spin measurements. Lastly, compared with two-body interactions (2BIs), in the presence of cavity losses and single particle decoherence, 3BIs feature a high gain in sensitivity for moderate atom numbers and in large ensembles a fast entanglement generation despite constraints in parameter regimes where they are implementable.
@article{arxiv.2512.06170,
title = {Collective three-body interactions enable a robust quantum speedup},
author = {Haoqing Zhang and Anjun Chu and Chengyi Luo and Chitose Maruko and Eliot A. Bohr and James K. Thompson and Ana Maria Rey},
journal= {arXiv preprint arXiv:2512.06170},
year = {2025}
}