标题： 三位一体的三量子比特Veldkamp线：引力和黑洞熵形式理论的有限几何基础 显示英文标题

标题： The magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy

摘要： 我们研究三量子比特魔力维德坎普线（MVL）的结构。 这一数学概念最近作为理解梅尔明五边形集合结构的工具出现，这些对象被用来排除某些隐变量理论的类别。 在这里，我们表明这个对象还为理解引力和黑洞熵的形式理论中使用的泛函结构提供了统一的有限几何基础。 我们澄清了我们MVL不同部分的表示理论、有限几何和物理意义。 我们考虑的结果是，使MVL在物理应用上具有如此多样性的基本有限几何对象是唯一的具有三个点的广义四边形，它们的一个点扩展以及与其同构于三阶二阶仿射极空间的其他扩展。 在之前的工作中，我们已经将广义四边形与五维黑洞和弦的熵公式相关的立方约当代数结构联系起来。 在某种程度上，本文可以被视为对该分析的推广，同时也提供了对四维黑洞熵公式的有限几何理解。 然而，我们发现许多结构的物理意义尚待探索。 作为熟悉的特例，我们的工作提供了从立方约当代数到基于这些代数的弗洛登塔尔系统的代数扩张的有限几何表示。 显示英文摘要

摘要： We investigate the structure of the three-qubit magic Veldkamp line (MVL). This mathematical notion has recently shown up as a tool for understanding the structures of the set of Mermin pentagrams, objects that are used to rule out certain classes of hidden variable theories. Here we show that this object also provides a unifying finite geometric underpinning for understanding the structure of functionals used in form theories of gravity and black hole entropy. We clarify the representation theoretic, finite geometric and physical meaning of the different parts of our MVL. The upshot of our considerations is that the basic finite geometric objects enabling such a diversity of physical applications of the MVL are the unique generalized quadrangles with lines of size three, their one point extensions as well as their other extensions isomorphic to affine polar spaces of rank three and order two. In a previous work we have already connected generalized quadrangles to the structure of cubic Jordan algebras related to entropy fomulas of black holes and strings in five dimensions. In some respect the present paper can be regarded as a generalization of that analysis for also providing a finite geometric understanding of four-dimensional black hole entropy formulas. However, we find many more structures whose physical meaning is yet to be explored. As a familiar special case our work provides a finite geometric representation of the algebraic extension from cubic Jordan algebras to Freudenthal systems based on such algebras.