AI 中文总结
研究Wands对偶性在准德西特背景中如何体现在原初扰动的实空间量子关联上，发现协方差矩阵的辛特征值及其导出的纠缠度量在对偶实现中一致，揭示了德西特真空的新量子信息对称性。
AI 中文摘要
我们研究了准德西特背景中的简并性（在Wands对偶意义上）如何体现在原初扰动的实空间量子关联中。利用粗粒化标量涨落的连续变量高斯形式，我们构建了暴胀时空中一对空间局域模的协方差矩阵，并提取了系统的辛不变量。对于一般的Wands对偶背景对，我们发现虽然协方差矩阵的各个条目高度依赖于背景，但辛特征值——以及纠缠熵、互信息、量子失谐和对数负性——在两个对偶实现中完全一致。我们的结果揭示了德西特真空的一种新的“量子信息对称性”，根据该对称性，由粗粒化场构造的局域线性纠缠见证无法区分Wands对偶的暴胀历史，即使它们的背景轨迹不同。我们证明，Wands对偶对称性的特殊性质（作为局域、尺度无关的正则变换）是这种对偶的核心。
英文摘要
We investigate how degeneracies in quasi-de Sitter backgrounds, in the sense of Wands' duality, are reflected in real-space quantum correlations of primordial perturbations. Using the continuous-variable Gaussian formalism for coarse-grained scalar fluctuations, we construct the covariance matrix of a pair of spatially localized modes in inflationary spacetime, and extract the symplectic invariants of the system. For a generic Wands-dual pair of backgrounds, we find that while the individual entries of the covariance matrix are highly background-dependent, the symplectic eigenvalues -- and hence the entanglement entropy, mutual information, quantum discord and log-negativity -- all coincide for the two dual realizations. Our results unveil a new ''quantum-informatic symmetry'' of the de Sitter vacuum, according to which local linear entanglement witnesses constructed from coarse-grained fields cannot distinguish between Wands-dual inflationary histories, even though their background trajectories differ. We show that the special nature of the Wands-duality symmetry (of being local, scale-independent canonical transformations) is at the heart of this duality.
Comments20 pages, 3 figures
