In this work, we establish a so-called "system-bath entanglement theorem," for arbitrary systems coupled with Gaussian environments. This theorem connects the entangled system-bath response functions in the total composite space to those of local systems, as long as the interacting bath spectral densities are given. We validate the theorem with direct evaluation via the exact dissipaton-equation-of-motion approach. Therefore, this work enables various quantum dissipation theories, which originally describe only the reduced system dynamics, for their evaluations on the system-bath entanglement properties. Numerical demonstrations are carried out on the Fano interference spectroscopies of spin-boson systems.

中文翻译：

---

高斯环境下的系统浴纠缠定理。

在这项工作中，我们为与高斯环境耦合的任意系统建立了一个所谓的“系统浴缠结定理”。只要给出相互作用的浴光谱密度，该定理就将整个复合空间中纠缠的系统-浴响应函数与局部系统的纠缠联系起来。我们通过精确的耗散运动方程法通过直接评估来验证该定理。因此，这项工作启用了各种量子耗散理论，这些理论最初仅描述了降低的系统动力学，用于评估系统-浴的纠缠特性。对自旋玻色子系统的Fano干涉光谱进行了数值论证。