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arXiv · 2010.11891

Can entanglement hide behind triangle-free graphs?

Satvik Singh
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Abstract

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.

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Satvik Singh. 2021-03-29. Can entanglement hide behind triangle-free graphs?. https://doi.org/10.1103/physreva.103.032436

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