论文标题
超图和稳定器熵锥之间的缝隙
A Gap Between the Hypergraph and Stabilizer Entropy Cones
论文作者
论文摘要
最近发现，四个政党的稳定剂和超图熵锥重合，导致他们在较高的政党数字上的等价性猜想。在本说明中，我们通过证明所有超图形熵向量遵守的新不平等现象，这些猜想是错误的，这些熵向六个量子位上的特定稳定器状态排除了。通过进一步利用这种联系，我们提高了稳定器熵的表征，并表明除经典单调性外，所有线性等级的不平等现象是稳定器锥的形式。此外，通过研究超图表的最小削减，我们证明了纠缠的超图表的某些结构特性，并概括了全息图中纠缠楔形嵌套的概念。
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 minimum cuts on hypergraphs, we prove some structural properties of hypergraph representations of entanglement and generalize the notion of entanglement wedge nesting in holography.
