We show that the states generated by a three-mode spontaneous parametric down-conversion (SPDC) interaction Hamiltonian possess tripartite entanglement of a different nature to other paradigmatic three-mode entangled states generated by the combination of two-mode SPDC interactions. While two-mode SPDC generates Gaussian states whose entanglement can be characterized by standard criteria based on two-mode quantum correlations, these criteria fail to capture the entanglement generated by three-mode SPDC. We use criteria built from three-mode correlation functions to show that the class of states recently generated in a superconducting-circuit implementation of three-mode SPDC ideally have tripartite entanglement, contrary to recent claims in the literature. These criteria are suitable for triple SPDC but we show that they fail to detect tripartite entanglement in other states which are known to possess it, which illustrates the existence of two fundamentally different notions of tripartite entanglement in three-mode continuous-variable systems.

中文翻译：

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三模自发参数下转换中的三方真非高斯纠缠。

我们表明，由三模式自发参数下转换（SPDC）相互作用哈密顿量生成的状态具有与其他通​​过两模式SPDC交互作用生成的范式三模式纠缠态不同性质的三方纠缠。虽然双模SPDC生成高斯态，其纠缠度可以通过基于双模量子相关性的标准判据来表征，但这些判据无法捕获三模SPDC所产生的纠缠。我们使用从三模相关函数构建的标准来表明，在三模SPDC的超导电路实现中最近生成的状态类别理想地具有三方纠缠，这与文献中最近的说法相反。