用强化学习找全息熵锥的边界，发现6个神秘射线中3个可实现，3个不可行
Exploring the holographic entropy cone via reinforcement learning
- 用强化学习搜索图结构，使最小割熵匹配目标熵向量
- 在N=6时找到3个神秘射线的图实现，证明其为真实极射线
- 剩余3个不可实现，暗示存在未被发现的全息熵不等式
我们开发了一种强化学习算法来研究全息熵锥。给定一个目标熵向量，该算法寻找一个图实现，使其最小割熵与目标向量一致。若目标向量无法实现，则说明它位于锥外，此时算法会找到最接近的目标图实现，从而探测锥的面位置。对于N=3情形，我们确认算法能从锥外目标重新发现量子关联的单性原理。随后将该算法应用于N=6情形，分析arXiv:2412.15364中6个满足所有已知全息熵不等式但缺乏图实现的“谜题”极端射线。我们成功找到了其中3个的图实现，证明它们是全息熵锥的真实极射线；而对另外3个提供了不可实现的证据，表明N=6时存在未知的全息熵不等式。
原文摘要 · Abstract (English)
We develop a reinforcement learning algorithm to study the holographic entropy cone. Given a target entropy vector, our algorithm searches for a graph realization whose min-cut entropies match the target vector. If the target vector does not admit such a graph realization, it must lie outside the cone, in which case the algorithm finds a graph whose corresponding entropy vector most nearly approximates the target and allows us to probe the location of the facets. For the $\sf N=3$ cone, we confirm that our algorithm successfully rediscovers monogamy of mutual information beginning with a target vector outside the holographic entropy cone. We then apply the algorithm to the $\sf N=6$ cone, analyzing the 6 "mystery" extreme rays of the subadditivity cone from arXiv:2412.15364 that satisfy all known holographic entropy inequalities yet lacked graph realizations. We found realizations for 3 of them, proving they are genuine extreme rays of the holographic entropy cone, while providing evidence that the remaining 3 are not realizable, implying unknown holographic inequalities exist for $\sf N=6$.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。