桥图中的量子最大流

Pub Date : 2024-07-03 DOI:10.1007/s00031-024-09863-2

Fulvio Gesmundo, Vladimir Lysikov, Vincent Steffan

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引用次数: 0

摘要

量子最大流是经典图最大流的线性代数版本，在量子多体物理学中用于量化张量网络状态两个区域之间可能存在的最大纠缠。在这项工作中，我们精确计算了桥图情况下的量子最大流。这一结果是通过与前同质张量空间理论和振子表示理论的联系得出的。此外，我们还强调了与不变理论和代数统计的关系。

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Quantum Max-flow in the Bridge Graph

The quantum max-flow is a linear algebraic version of the classical max-flow of a graph, used in quantum many-body physics to quantify the maximal possible entanglement between two regions of a tensor network state. In this work, we calculate the quantum max-flow exactly in the case of the bridge graph. The result is achieved by drawing connections to the theory of prehomogenous tensor spaces and the representation theory of quivers. Further, we highlight relations to invariant theory and to algebraic statistics.

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