来自大家族的婴儿宇宙：小册子宇宙态与量子纠错

中文摘要 AI 辅助

我们提出将Antonini、Sasieta和Swingle（AS$^2$）的宇宙态构造扩展到三个或更多全息CFT。每个CFT位于一个AdS页面的渐近边界上，所有页面通过施加多路结条件沿公共接口粘合。相关态由具有多线性插入的欧几里得演化制备。在适当的重插入极限下，体几何在中心发展出一个闭合宇宙，我们将此极限下的态称为小册子宇宙态。扩展AS$^2$中使用的有效高斯假设，我们将三页插入建模为圆形复高斯随机张量，在平坦能量窗口中产生三部分Haar态。在这个宇宙到边界映射的高斯模型中，每个臂是与一个边界CFT相关联的网络分支。在三个页面具有三个相等输出希尔伯特空间维度$b$的最简单例子中，我们证明一个维度为$K$的规定码可从任意两个臂近似恢复，当$K/b\ o0$时，误差趋于零且概率很高。

英文摘要

We propose an extension of the cosmological-state construction of Antonini, Sasieta and Swingle (AS$^2$) to three or more holographic CFTs. Each CFT resides on the asymptotic boundary of an AdS page, and all pages are glued along a common interface by imposing the multiway junction conditions. The associated states are prepared by Euclidean evolution with a multilinear insertion. In appropriate heavy insertion limit the bulk geometry develop a closed universe in the center and we refer the state in this limit as a booklet cosmological state. Extending the effective Gaussian assumption used in AS$^2$, we model the three-page insertion by a circular complex Gaussian random tensor, yielding a tripartite Haar state in flat energy windows. In this Gaussian model of the cosmology-to-boundary map, each arm is a network branch associated with one boundary CFT. In the simplest example of three pages with three equal output Hilbert-space dimension $b$, we show that a prescribed code of dimension $K$ is approximately recoverable from any two arms, with vanishing error and high probability as $K/b\to0$.

发表机构

• University of the Chinese Academy of Sciences（中国科学院大学）
• Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）
• Peng Huanwu Center for Fundamental Theory（彭桓武理论研究中心）

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