论文标题
超图的量子熵锥
The Quantum Entropy Cone of Hypergraphs
论文作者
论文摘要
在这项工作中，我们概括了用于研究超图及其类似定义的熵锥的全息熵锥所用的图理论技术。这使我们能够开发一个框架，以有效地计算熵并证明超图满足。在此过程中，我们发现了一类量子熵向量，这些向量超出了全息态的量子，并遵守与稳定剂状态和线性等级遵守的量子的约束密切相关。我们表明，至少多达4个政党，超图锥与稳定器熵锥相同，因此表明该超雕像框架广泛适用于纠缠熵的研究。我们猜想，这种平等继续持有更高的政党人数，并在这个方向上报告了部分进展。为了物理激励这种猜想的等效性，我们还提出了一种受张量网络启发的合理方法，以从给定的超图构建量子状态，以使其熵向量匹配。
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 demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy. We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction. To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match.
