School of Physics and Information Engineering, Shanxi Normal University, Taiyuan 030031, China.
Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 place Jussieu, F-75252 Paris, France.
Phys Rev Lett. 2023 Mar 3;130(9):093602. doi: 10.1103/PhysRevLett.130.093602.
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.
三光子态由三模自发参量下转换产生，是无条件非高斯态的范例，是量子优势的关键资产。然而，如何充分描述它们的非高斯纠缠仍然难以捉摸。在这里，我们提出了一套充分必要条件，用于分离广泛的自发产生的三模非高斯态。我们进一步推导出真正的三方非高斯纠缠的最新条件，这是最强的纠缠类。我们将我们的标准应用于三光子态，结果表明，它们在 3n 阶矩处是完全不可分离的，并且是真正纠缠的。我们的结果为三光子态的纠缠特性建立了一个系统的框架，从而促进了它们在量子信息协议中的应用。
