Hypergraph min-cuts from quantum entropies

A Gap Between the Hypergraph and Stabilizer Entropy Cones

It was recently found that the stabilizer and hypergraph entropy cones coincide for four parties, leading to a conjecture of their equivalence at higher party numbers. In this note, we show this conjecture to be false by proving new inequalities obeyed by all hypergraph entropy vectors that exclude particular stabilizer states on six qubits. By further leveraging this connection, we improve the characterization of stabilizer entropies and show that all linear rank inequalities at five parties, except for classical monotonicity, form facets of the stabilizer cone. Additionally, by studying mini…

The Quantum Entropy Cone of Hypergraphs

In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone. This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs. In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks. We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus dem…

随机张量网络中的多熵

Multi-entropy in random tensor networks

研究随机张量网络态中Rényi多熵的评估，证明对于n=2时多熵由最小多路割决定，并给出退化情况下的刻画；对于n>2则通过反例否定最小多路割猜想。

随机张量网络中的反射熵 III：三向切割

Reflected entropy in random tensor networks III: triway cuts

针对大键维数随机张量网络态，证明了整数Rényi反射熵由最小三向切割决定，并由此揭示全息态中三部分纠缠与二分纠缠结构间的差距。

量子超图态的魔性（Magic）

Magic of quantum hypergraph states

本文系统解析研究量子超图态的魔性资源，给出通用魔性公式，证明随机超图态通常可达最大魔性，而高对称超图态魔性极低，推进了多体量子魔性的理解。

超图稀疏化的量子加速

Quantum Speedup for Hypergraph Sparsification

针对超图稀疏化问题，提出了首个运行时间为$\widetilde O(r\sqrt{mn}/\varepsilon)$的量子算法，匹配常数秩下的量子下界，并实现了对经典算法的量子加速。