Hierarchy of Genuine Tripartite Non-Gaussian Entanglement

TL;DR

This paper develops a systematic hierarchy of criteria to fully characterize and detect genuine tripartite non-Gaussian entanglement in triple-photon states, advancing quantum information applications.

Contribution

It introduces a hierarchy of necessary and sufficient conditions for separability and entanglement in three-mode non-Gaussian states, specifically applied to triple-photon states.

Findings

Triple-photon states are fully inseparable and genuinely entangled at moments of order 3n.

The criteria effectively detect genuine tripartite non-Gaussian entanglement.

The framework aids in the systematic characterization of entanglement in non-Gaussian states.

Abstract

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.