论文标题
纠缠无三角形的图形可以隐藏吗？
Can entanglement hide behind triangle-free graphs?
论文作者
论文摘要
我们提出了一种替代方法，以在两分量子状态下揭示另一种纠缠，其对角零模式在合适的矩阵表示中的零模式接受了很好的描述，从无三角形的图表中进行了很好的描述。在应用局部平均操作后，这种状态的可分离性转化为简单的矩阵阳性条件，违反该条件意味着纠缠的存在。我们完全表征了无三角形图的类别，这些图允许使用上述测试进行非平凡的纠缠检测。此外，我们开发了一个配方，以在任意维度中构建大量独特的积极部分转置（PPT）无三角形状态。最后，我们将一般状态中纠缠检测的任务与在给定图中找到无三角形诱导的子图的众所周知的图理论问题联系起来。
We present an alternative approach to unveil a different kind of entanglement in bipartite quantum states whose diagonal zero patterns in suitable matrix representations admit a nice description in terms of triangle-free graphs. Upon application of a local averaging operation, the separability of such states transforms into a simple matrix positivity condition, the violation of which implies the presence of entanglement. We completely characterize the class of triangle-free graphs which allows for nontrivial entanglement detection using the above test. Moreover, we develop a recipe to construct a plethora of unique classes of positive partial transpose (PPT) entangled triangle-free states in arbitrary dimensions. Finally, we link the task of entanglement detection in general states to the well-known graph-theoretic problem of finding triangle-free-induced subgraphs in a given graph.
