We introduce families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan subalgebra elements and by applying these unitaries to regular group-theoretic coherent states. This enables us to generate entanglement not found in the coherent states themselves, while retaining many of their desirable properties. Most importantly, we explain how the expectation values of physical observables can be evaluated efficiently. Examples include generalized spin-coherent states and generalized Gaussian states, but our construction can be applied to any Lie group represented on the Hilbert space of a quantum system. We comment on their applicability as variational families in condensed matter physics and quantum information.

中文翻译：

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群论相干态的泛化计算泛化

我们介绍了在著名的Gilmore-Perelomov群理论相干态之上构建的纯量子态族。为此，我们将unit元构造为Cartan子代数元素中二次方算子的指数，并将这些unit元应用于规则的群论相干态。这使我们能够生成相干态本身未发现的纠缠，同时保留它们的许多理想特性。最重要的是，我们解释了如何有效评估物理可观测值的期望值。例子包括广义自旋相干态和广义高斯态，但是我们的构造可以应用于在量子系统的希尔伯特空间上表示的任何李群。