论文标题
组和非本地游戏的光谱差距和稳定性
Spectral gap and stability for groups and non-local games
论文作者
论文摘要
当几乎满足方程的数学对象与完全满足的对象接近时，该单词稳定词用于描述一种情况。我们研究了对群体的单一表示和非本地游戏的量子同步策略的稳定性的操作员形式。我们特别观察到简单的光谱差距估计可以导致强大的稳定性定量形式。例如，我们证明了两个（灵活的）Hilbert-Schmidt稳定组的直接乘积再次（灵活地）Hilbert-Schmidt稳定，但前提是其中一个具有Kazhdan的特性（T）。我们还提供了对非本地游戏的简单形式和简单的分析，其中几乎没有问题，其属性具有较大价值的同步策略接近涉及大型Pauli矩阵的完美策略。这简化了JI，Natarajan，Vidick，Wright和Yuen最近宣布的Connes嵌入问题的解决方案之一。
The word stable is used to describe a situation when mathematical objects that almost satisfy an equation are close to objects satisfying it exactly. We study operator-algebraic forms of stability for unitary representations of groups and quantum synchronous strategies for non-local games. We observe in particular that simple spectral gap estimates can lead to strong quantitative forms of stability. For example, we prove that the direct product of two (flexibly) Hilbert-Schmidt stable groups is again (flexibly) Hilbert-Schmidt stable, provided that one of them has Kazhdan's property (T). We also provide a simple form and simple analysis of a non-local game with few questions, with the property that synchronous strategies with large value are close to perfect strategies involving large Pauli matrices. This simplifies one of the steps (the question reduction) in the recent announced resolution of Connes' embedding problem by Ji, Natarajan, Vidick, Wright and Yuen.
