交叉与锁定：比特线程与连续多重流
Crossing versus locking: Bit threads and continuum multiflows
AI总结：
本文研究全息时空中比特线程在不同密度约束下的锁定条件，证明最严格约束下非交叉区域可锁定、交叉区域不可，较宽松约束下交叉对可锁定，并提出无两两交叉三元组的区域集可锁定的猜想。
摘要：
比特线程是全息时空中体现边界纠缠的曲线，在数学上由网络流或多重流的连续类似物表示。在密度约束下，连接边界区域与其补集的最大线程数可计算Ryu-Takayanagi熵。当同时考虑多个区域时（例如在证明熵不等式时），可以施加多种不等价的密度约束。我们研究了在何种约束选择下，一组给定的边界区域可以被“锁定”，即它们的熵可以通过单个线程构型计算。我们证明，在要求线程局部平行的最严格约束下，非交叉区域通常可以被锁定，但交叉区域不能；其中两个区域被定义为交叉，当它们部分重叠且不覆盖整个边界。我们还证明，在某一较宽松的密度约束下，一对交叉区域可以被锁定，并猜想任何不包含两两交叉三元组的区域集合都可以被锁定，这与网络中的情况类似。
英文摘要：
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.
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