论文标题
全息图中的多部分纠缠和拓扑
Multipartite entanglement and topology in holography
论文作者
论文摘要
从多部分混合状态的纠缠楔开始，我们描述了一种纯化程序，其中涉及几个副本的粘合。所得的几何形状具有非平凡的拓扑结构和每个原始边界区域的单个方向边界。在纯化的几何形状中，原始的多部分纠缠楔横截面被映射到特定非平凡同源性类别的最小表面。相比之下，每个原始的两部分纠缠楔形截面都映射到每个边界周围的最小虫洞喉咙。使用位螺纹形式主义，我们显示了如何将两分和多部分纠缠楔横截面的最大流胶合在一起，以在纯化的几何形状中形成最大多量。定义特征区分流程是由线程的存在给出的，这些线程在原始纠缠楔的不同副本之间交叉。这些共同证明了多部分纠缠与全息空间拓扑之间的可能联系。
Starting from the entanglement wedge of a multipartite mixed state we describe a purification procedure which involves the gluing of several copies. The resulting geometry has non-trivial topology and a single oriented boundary for each original boundary region. In the purified geometry the original multipartite entanglement wedge cross section is mapped to a minimal surface of a particular non-trivial homology class. In contrast each original bipartite entanglement wedge cross section is mapped to the minimal wormhole throat around each boundary. Using the bit thread formalism we show how maximal flows for the bipartite and multipartite entanglement wedge cross section can be glued together to form maximal multiflows in the purified geometry. The defining feature differentiating the flows is given by the existence of threads which cross between different copies of the original entanglement wedge. Together these demonstrate a possible connection between multipartite entanglement and the topology of holographic spacetimes.
