发表机构
Rikkyo University; RIKEN; Perimeter Institute for Theoretical Physics（立教大学; 理化学研究所; 理论物理前沿研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出纠缠相对熵的全息对偶，以最小体三方曲面与AB同调最小曲面面积差表示，并在随机张量网络中证明上下界，揭示三叉结几何结构。
AI 中文摘要
我们提出了边界三方划分$A:B:C$的纠缠相对熵的全息对偶。我们的提议是，在领头阶，\begin{align} E_R(\rho_{AB}) = \frac{1}{4G_N}\big[\text{Area}(\Gamma_{\min}) - \text{Area}(\gamma_{AB})\big] \notag \end{align} 其中$\Gamma_{\min}$是最小体三方曲面，$\gamma_{AB}$是与$AB$同调的最小曲面。对于一般的随机张量网络，我们通过构造与$\Gamma_{\min}$关联的可分离态并评估其相对熵来证明相应的上界。我们还严格地为包含一个、两个和三个Haar随机张量的网络建立了匹配的下界，通过限制最大三方乘积态重叠。在适当的几何中，最小三方曲面可以形成一个非平凡的类似Mercedes标志的三叉结。证明过程通过对候选乘积态的顺序优化进行，这具有作为最小三方曲面的局部搜索的自然几何解释。
英文摘要
We propose a holographic dual of the relative entropy of entanglement for a boundary tripartition $A:B:C$. Our proposal is that, at the leading order, \begin{align} E_R(ρ_{AB}) = \frac{1}{4G_N}\Big[\mathrm{Area}(Γ_{\min}) - \mathrm{Area}(γ_{AB})\Big] \notag \end{align} where $Γ_{\min}$ is the minimal bulk tripartition surface and $γ_{AB}$ is the minimal surface homologous to $AB$. For a general random tensor network, we prove the corresponding upper bound by constructing a separable state associated with $Γ_{\min}$ and evaluating its relative entropy. We also establish the matching lower bound rigorously for networks of one, two, and three Haar random tensors by bounding the maximal tripartite product-state overlap. In appropriate geometries, the minimal tripartition surface can form a nontrivial tri-junction resembling the Mercedes logo. The proof proceeds by sequential optimization over candidate product states, which has a natural geometric interpretation as a local search for the minimal tripartition surface.
Comments53 pages, many figures
