多不变量中的单调量：一个分类
Monotones from multi-invariants: the Coxeter classification
AI总结：
本文研究多部分量子态在LOCC下单调的局域酉不变量，猜想边凸多不变量由有限Coxeter群分类，并证明了除六种情况外的所有情形。
摘要：
本文研究了多部分量子态在局域操作与经典通信（LOCC）下平均意义上单调的局域酉不变量。我们特别关注由态及其共轭的多项式构造的局域酉不变量，称为多不变量。多不变量由特定类型的图标记。最近，在文献[Gadde:2024jfi]中，作者将LOCC下的单调性条件与多不变量上的一个图论条件——边凸性——联系起来。本文我们猜想边凸多不变量的完全分类。该猜想指出，边凸多不变量由有限Coxeter群标记。我们证明了除六种情况外的所有情形。
英文摘要：
Multi-invariants are multiplicative polynomial invariants of multipartite pure states under local unitaries. They yield entanglement monotones when their contraction graphs satisfy edge-convexity. We classify all connected edge-convex multi-invariants. Up to duplication of entire edge-colour families, their contraction graphs are precisely the standard edge-labelled Cayley graphs of finite Coxeter systems. Necessity follows by identifying edge-reflecting graphs with Coxeter Cayley graphs. For sufficiency, we prove vertex-convexity of parabolic quotients and lift their matrices by induction. This covers all classical and exceptional families. For the largest quotients, $E_8/D_7$ and $H_4/A_3$, wall symmetry reduces the matrices to exact positivity tests over $\mathbb Q$ and $\mathbb Q(\sqrt5)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
