Genuine Tripartite Non-Gaussian Entanglement

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 set 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.

Figure 1

Evolution of $F_1^n$ (a) and $W_n$ (b) as a function of the interaction strength $\xi$. $F_1^n<0$ and $W_n<0$ indicate full inseparability and genuine entanglement, respectively. $\xi =\kappa {\alpha }_{p}t$ and ${\alpha }_p=\sqrt{25}$. Note that $F_1^n=F_2^n=F_3^n$.