Triple-photon states generated by three-mode spontaneous parametric down-conversion are the paradigm of unconditional non-Gaussian states, essential assets for quantum advantage. How to fully characterize their non-Gaussian entanglement remains however elusive. We propose here a hierarchy of sufficient and necessary conditions for separability of the broad family of spontaneously-generated three-mode non-Gaussian states. We further derive state-of-the-art conditions for genuine tripartite non-Gaussian entanglement, the strongest class of entanglement. We apply our criteria to triple-photon states revealing that they are fully inseparable and genuinely entangled in moments of order 3n. Our results establish a systematic framework for characterizing the entanglement of triple-photon states and thus fostering their application in quantum information protocols.
@article{arxiv.2205.11940,
title = {Hierarchy of Genuine Tripartite Non-Gaussian Entanglement},
author = {Da Zhang and David Barral and Yanpeng Zhang and Min Xiao and Kamel Bencheikh},
journal= {arXiv preprint arXiv:2205.11940},
year = {2023}
}