Entanglement witnesses based on first and second moments exist in the form of spin squeezing criteria for the detection of particle entanglement from collective measurements, and in the form of modified uncertainty relations for the detection of mode entanglement or steering. By revealing a correspondence between them, we show that metrologically useful spin squeezing reveals multimode entanglement in symmetric spin states that are distributed into addressable modes. We further derive tight state-independent multipartite entanglement bounds on the spin squeezing coefficient and point out their connection to widely used entanglement criteria that depend on the state's polarization. Our results are relevant for state-of-the-art experiments where symmetric entangled states are distributed into a number of addressable modes, such as split spin squeezed Bose-Einstein condensates.

中文翻译：

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将自旋压缩与粒子和模式的多部分缠结标准相关

基于第一刻和第二刻的纠缠证人以自旋挤压标准的形式存在，用于从集体测量中检测粒子的纠缠，并以修正的不确定性关系的形式存在，以用于检测模式的纠缠或操纵。通过揭示它们之间的对应关系，我们证明了在计量上有用的自旋压缩揭示了在对称自旋状态下的多模纠缠，这些对称自旋状态分布在可寻址模式中。我们进一步推导自旋压缩系数上与状态无关的紧密多方纠缠边界，并指出它们与依赖于状态极化的广泛使用的纠缠准则的联系。我们的结果与将对称纠缠态分布到许多可寻址模式中的最新实验有关，