In this paper, we study the construction of classical geometry from the quantum entanglement structure by using information geometry. In the information geometry of classical spacetime, the Fisher information metric is related to a blurred metric of a classical physical space. We first show that a local information metric can be obtained from the entanglement contour in a local subregion. This local information metric measures the fine structure of entanglement spectra inside the subregion, which suggests a quantum origin of the information-geometric blurred space. We study both the continuous and the classical limits of the quantum-originated blurred space by using the techniques from the statistical sampling algorithms, the sampling theory of spacetime and the projective limit. A scheme for going from a blurred space with quantum features to a classical geometry is also explored.

中文翻译：

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纠缠中的空间：信息几何视角

在本文中，我们利用信息几何研究从量子纠缠结构构建经典几何。在经典时空的信息几何中，Fisher 信息度量与经典物理空间的模糊度量有关。我们首先表明可以从局部子区域中的纠缠轮廓中获得局部信息度量。这种局部信息度量测量子区域内纠缠光谱的精细结构，这表明信息几何模糊空间的量子起源。我们利用统计采样算法、时空采样理论和射影极限等技术研究了量子起源模糊空间的连续极限和经典极限。