论文标题
交叉与锁定：位线程和连续性多曲线
Crossing versus locking: Bit threads and continuum multiflows
论文作者
论文摘要
位线是表现边界纠缠的全息空间中的曲线，并由网络流或多插槽的连续类似物在数学上表示。受密度结合的约束，将边界区域连接到其补充的最大线程计算Ryu-takayanagi熵。当同时考虑几个区域时，例如在证明熵不等式时，可以施加的各种不相等密度界限。我们研究了哪些绑定的给定边界区域的选择可以“锁定”，换句话说，可以通过单个线程配置计算其熵。我们表明，在最严格的界限下，要求线程在局部并行，通常可以锁定不交叉的区域，但是越过区域不能，如果有两个区域的部分重叠，并且不覆盖整个边界，则越过区域不能。我们还表明，在某些不太严格的密度绑定下，可以锁定交叉对，并猜测任何不包含成对交叉三重的区域都可以锁定，类似于网络的情况。
Bit threads are curves in holographic spacetimes that manifest boundary entanglement, and are represented mathematically by continuum analogues of network flows or multiflows. Subject to a density bound, the maximum number of threads connecting a boundary region to its complement computes the Ryu-Takayanagi entropy. When considering several regions at the same time, for example in proving entropy inequalities, there are various inequivalent density bounds that can be imposed. We investigate for which choices of bound a given set of boundary regions can be "locked", in other words can have their entropies computed by a single thread configuration. We show that under the most stringent bound, which requires the threads to be locally parallel, non-crossing regions can in general be locked, but crossing regions cannot, where two regions are said to cross if they partially overlap and do not cover the entire boundary. We also show that, under a certain less stringent density bound, a crossing pair can be locked, and conjecture that any set of regions not containing a pairwise crossing triple can be locked, analogously to the situation for networks.
