发表机构
University of California, Davis; Tsinghua University; Ecole Polytechnique Federale de Lausanne (EPFL)（加州大学戴维斯分校; 清华大学; 洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文猜想并证明两个无限全息熵不等式族均可改写为三部分形式，提供显式表达式并推导有用恒等式，展示该形式在证明结构性质中的威力。
AI 中文摘要
为了阐明全息熵不等式（超越次可加性）的含义，这些不等式刻画了全息中几何态的纠缠结构，arXiv:2309.06296 提出了这些不等式的“三部分形式”，由三部分信息和条件三部分信息项组成，系数为单位系数。虽然这为不等式提供了一种紧凑且有用的封装，但并非先验地保证所有不等式都能改写为此形式。在此我们猜想它们可以，并通过证明 arXiv:2309.15145 中发现的两个已知的无限全息熵不等式族确实可以写成三部分形式，提供了大量证据。这一点意义重大，因为对于这些族而言，这种改写尤其非平凡。除了为这两个无限族的每个成员提供显式的三部分形式表达式外，我们还详细说明了我们如何得到这些表达式，在此过程中推导出几个有用的恒等式，这些恒等式可作为进一步重新封装相应信息量的垫脚石。我们还通过证明任何全息熵不等式满足的若干结构性质，展示三部分形式的力量。
英文摘要
To elucidate the meaning of holographic entropy inequalities (beyond subadditivity) which characterize the entanglement structure of geometric states in holography, arXiv:2309.06296 proposed the "tripartite form" for these inequalities, consisting of tripartite information and conditional tripartite information terms with unit coefficients. While this provides a compact and useful packaging of the inequalities, it is not a priori guaranteed that all inequalities can be recast in this form. Here we conjecture that they can, and present substantial evidence, by proving that the two known infinite families of holographic entropy inequalities found in arXiv:2309.15145 can indeed be written in the tripartite form. This is significant because such recasting is particularly nontrivial for these families. Apart from providing the explicit tripartite form expressions for every member of these two infinite families, we detail how we arrived at them, in the process deriving several useful identities which may serve as stepping stones to formulate further repackaging of the corresponding information quantities. We also illustrate the power of the tripartite form by proving a number of structural properties satisfied by any holographic entropy inequality.
Comments47 pages, 5 figures
