The symmetric cascaded four‐wave mixing process is a phase‐insensitive and easy‐to‐implement technology to prepare quadripartite entanglement. However, it has not yet been discussed whether the state generated by this method is genuinely entangled. Here, it is shown that the genuine quadripartite entanglement criteria previously derived are not applicable to the symmetric cascaded scheme. Thus some more effective sufficient conditions are derived for detecting genuine entanglement in this work. The existence of genuine quadripartite entanglement is then confirmed through different entanglement witnesses. Under the premise that the quadripartite state is genuinely entangled, the quantum gain of the first‐stage determines the optimal range of the quantum gain of second‐stage. Finally, it is show that the four output modes are genuinely entangled within the appropriate quantum gain ranges when the optical loss of each step of the cascaded system is less than 10%. The results pave the way for the experimental generation of genuine quadripartite entanglement in symmetric cascaded scheme.

中文翻译：

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对称级联四波混频过程中的真正四方连续可变纠缠

对称级联四波混频过程是一种不敏感且易于实现的技术，用于准备四方纠缠。但是，尚未讨论此方法生成的状态是否真正纠缠。在这里，表明先前推导的真正的四方纠缠标准不适用于对称级联方案。因此，得出了一些更有效的充分条件来检测这项工作中的真正纠缠。然后，通过不同的纠缠目击者证实了真正的四方纠缠的存在。在四方态真正纠缠的前提下，第一级的量子增益决定了第二级的量子增益的最佳范围。最后，结果表明，当级联系统每一步的光损耗小于10％时，四种输出模式确实在适当的量子增益范围内纠缠在一起。结果为对称级联方案中真实四方纠缠的实验生成铺平了道路。