发表机构
Brandeis University; Weizmann Institute of Science; Vrije Universiteit Brussel (VUB); The International Solvay Institutes（布兰迪斯大学; 魏茨曼科学研究所; 布鲁塞尔自由大学; 国际索尔维研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出量子协变比特线，以体流而非极值曲面表述全息纠缠熵，等价于量子极值曲面公式，为黑洞蒸发、岛屿和婴儿宇宙提供新视角。
AI 中文摘要
纠缠熵在全息原理中扮演核心角色。量子极值曲面（QES）公式是在动力学和体量子修正都很重要的情境（如黑洞蒸发）中的标准工具。我们推导并探索了与QES等价的处方——量子协变比特线——这些处方以最小或最大体流而非极值曲面来表述全息纠缠熵。与经典协变比特线类似，我们的处方有两种类型：（通常）类空的V流和类时的U流。为了考虑体量子修正，流线可以在体内的点开始和结束，其端点的分布由体纠缠熵控制。在我们的比特线语言中，QES是流的量子瓶颈，一些线穿过它（对应于广义熵中的面积项），而另一些线跳过它（对应于熵项）。我们的处方为QES公式提供了互补视角，并为黑洞蒸发、岛屿和婴儿宇宙等重要现象提供了新的见解。
英文摘要
Entanglement entropy plays a central role in holography. The quantum extremal surface (QES) formula is the standard tool in settings where both dynamics and bulk quantum corrections are important, such as in black hole evaporation. We derive and explore QES-equivalent prescriptions --- quantum covariant bit threads --- that formulate holographic entanglement entropy in terms of minimal or maximal bulk flows rather than extremal surfaces. Like classical covariant bit threads, our prescriptions come in two types: (typically) spacelike V-flows, and timelike U-flows. To account for bulk quantum corrections, the flow lines can start and end at points in the bulk, with the distribution of endpoints controlled by bulk entanglement entropies. In our bit thread language, the QES is a quantum bottleneck to the flow, with some threads passing through it (accounting for the area term in the generalized entropy) and others jumping across it (accounting for the entropy term). Our prescriptions provide a complementary perspective to the QES formula and offer new insights on important phenomena such as black hole evaporation, islands, and baby universes.
Comments43 pages. A four minute video abstract is available at https://youtu.be/8U8VdLAIku0
